Nominee (and results) list: http://www.thehugoawards.org/hugo-history/1945-retro-hugo-awards/
Now how to actually read them?
This ISFDB page is enormously handy: http://www.isfdb.org/cgi-bin/ay.cgi?34+2020
* The Golden Fleece, by Robert Graves (Cassell)
Ok, ISFDB doesn't even consider this to be SF. Its author rates a Wikipedia page, but the book doesn't, although it is mentioned as "historical fiction". Anyway, there's a 2017 edition, and others. No trouble to find, although I'm not sure why I should bother.
* Land of Terror, by Edgar Rice Burroughs (Edgar Rice Burroughs, Inc.)
Several reprintings. Easy.
* (winner) "Shadow Over Mars" (The Nemesis from Terra), by Leigh Brackett (Startling Stories, Fall 1944)
Not hard to find as "The Nemesis from Terra".
* Sirius: A Fantasy of Love and Discord, by Olaf Stapledon (Secker & Warburg)
Available in a newish volume along with Odd John, another Stapledon novel. Also not hard to find by itself.
* The Wind on the Moon, by Eric Linklater (Macmillan)
Easy to find.
* "The Winged Man", by A.E. van Vogt and E. Mayne Hull (Astounding Science Fiction, May-June 1944)
Easy to find. But note that the version you can find is substantially edited from the original 1944 story in Astounding. I haven't done a complete study, but the original is set on a WWII submarine while the novel you can buy is updated to a "mid-century" atomic sub. And for no obvious reason, instead of going forward in time 994,999 years, instead it is 24,999. The novel is also a good bit longer. You can read the originals at https://archive.org/details/Astounding_v33n03_1944-05_dtsg0318 and https://archive.org/details/Astounding_v33n04_1944-06_AK.
Of course, any of thse works may have been edited since their 1944 printing, but it is particularly likely for serials.
* "The Changeling", by A.E. van Vogt (Astounding Science Fiction, April 1944)
Available as a novel, several editions. Easy to find.
* "A God Named Kroo", by Henry Kuttner (Thrilling Wonder Stories, Winter 1944)
Apparently only ever reprinted in Fantastic Story Magazine, Summer 1954. Probably easiest to read the original at the Internet Archive: https://archive.org/details/Thrilling_Wonder_Stories_v25n02_1944-Winter
* "Intruders from the Stars", by Ross Rocklynne (Amazing Stories, January 1944)
Republished with "Flight of the Starling" in 2012. Three copies available on eBay in the $10-$20 range. you can also read the original: https://archive.org/details/Amazing_Stories_v18n01_1944-01_cape1736
* "The Jewel of Bas", by Leigh Brackett (Planet Stories, Spring 1944)
Republished several times. No single one seems to be the obvious one to get. The one with "Thieves' Carnival" from 1990 has a few available at a reasonable price on eBay, as do others.
* (winner) "Killdozer!", by Theodore Sturgeon (Astounding Science Fiction, November 1944)
Many reprintings. Maybe the easiest to get is in "The Mammoth Book of Golden Age Science Fiction".
* "Trog", by Murray Leinster (Astounding Science Fiction, June 1944)
Apparently never reprinted. Read it at https://archive.org/details/Astounding_v33n04_1944-06_AK
* "Arena", by Fredric Brown (Astounding Science Fiction, June 1944)
Reprinted many many times (http://www.isfdb.org/cgi-bin/title.cgi?41651). I read it in The Best of Fredric Brown. (Please note that the Star Trek episode is "based" on this story only in the loosest way, so don't vote for this based on how much you liked that episode.)
* "The Big and the Little" ("The Merchant Princes"), by Isaac Asimov (Astounding Science Fiction, August 1944)
This is one of the sections of Foundation. So you could read Foundation, but as with the previous sections, I recommend reading the original in Astounding: https://archive.org/details/Astounding_v33n06_1944-08_Gorgon776. I think the only changes are the usual "nuclear" for "atomic" (although interestingly the original has one "nuclear" I noticed; I wonder if it is because Asimov knew that was the correct term and would have used it if anyone else was) and some minor rewordings: the very end is longer by a few phrases and sentences; I bet that Campbell cut them to make it fit the page, so the later version may be closer to what Asimove wrote in the first place. (Interestingly, the printing of just "The Big and the Little" in The Mammoth Book of Golden Age Science Fiction retains "atomic", but has the long version of the ending, which probably confirms that theory.)
* "The Children's Hour", by Lawrence O'Donnell (C.L. Moore and Henry Kuttner) (Astounding Science Fiction, March 1944)
Republished thrice, including in Aliens from Analog and A Treasury of Great Science Fiction, Volume One, both of which are available at reasonable prices. You can also read the original on the Internet Archive: https://archive.org/details/Astounding_v33n01_1944-03_dtsg0318-LennyS
* (winner) "City", by Clifford D. Simak (Astounding Science Fiction, May 1944)
Republished many times (http://www.isfdb.org/cgi-bin/title.cgi?41546). The edition I read, and probably all others after the original printing, was slightly edited to add some additional commentary on the effects of the atom bomb. I don't think the differences are crucial, but you can read the original on the Internet Archive if you like: https://archive.org/details/Astounding_v33n03_1944-05_dtsg0318.
* "No Woman Born", by C.L. Moore (Astounding Science Fiction, December 1944)
Republished many times (http://www.isfdb.org/cgi-bin/title.cgi?47580). Edited to add: If you got the Mammoth Book of Golden Age Science Fiction as recommended above, you've already got this one too.
* "When the Bough Breaks", by Lewis Padgett (C.L. Moore and Henry Kuttner) (Astounding Science Fiction, November 1944)
Republished many times (http://www.isfdb.org/cgi-bin/title.cgi?189896).
* "And the Gods Laughed", by Fredric Brown (Planet Stories, Spring 1944)
Republished many times (http://www.isfdb.org/cgi-bin/title.cgi?61779). A lot of them are hardcover. Maybe the cheapest to get is Honeymoon in Hell.
* "Desertion", by Clifford D. Simak (Astounding Science Fiction, November 1944)
Since you have already bought the collection City above so you can read "City", you have this too now.
* "Far Centaurus", by A. E. van Vogt (Astounding Science Fiction, January 1944)
Republished many times (http://www.isfdb.org/cgi-bin/title.cgi?41417+1). Maybe the cheapest option is Starships, edited by Asimov.
* "Huddling Place", by Clifford D. Simak (Astounding Science Fiction, July 1944)
You already have this because you bought City.
* (winner) "I, Rocket", by Ray Bradbury (Amazing Stories, May 1944)
I guess this is one of those OMG BRADBURY nominations made by people who haven't read it. I put it as "maybe" on my list and then didn't nominate it in the end. It has been republished only three times, and one is an expensive hardcover whose title suggests a scholarly work. Probably cheapest to get in The Human Zero and Other Science-Fiction Masterpieces (1967) (one copy on eBay right now at $15), or since it's a short story, maybe just read the scans: https://archive.org/details/Amazing_Stories_v18n03_1944-05_cape1736
* "The Wedge" ("The Traders"), by Isaac Asimov (Astounding Science Fiction, October 1944)
This is a section of Foundation. See above. The original: https://archive.org/details/Astounding_v34n02_1944-10_dtsg0318-LennyS
I don't like this category. How am I supposed to know how to review a large body of work if I'm not already a fan of it? It's a dumb popularity contest category giving works almost no chance of being judged on their merits. Pass.
* Fancyclopedia, by Jack Speer (Forrest J. Ackerman)
You can read it in its entirety, converted to HTML here: https://fanac.org/Fannish_Reference_Works/Fancyclopedia/Fancyclopedia_I/, or the scans at http://www.fanac.org/Fannish_Reference_Works/Fancyclopedia/Fancyclopedia1.pdf.
* '42 To '44: A Contemporary Memoir Upon Human Behavior During the Crisis of the World Revolution, by H.G. Wells (Secker & Warburg)
Never reprinted. Available on eBay at $60 and up. Is this worth bothering?
* Mr. Tompkins Explores the Atom, by George Gamow (Cambridge University Press)
Get it in a volume literally called "Mr Tompkins in Paperback", available on eBay for under $5.
* Rockets: The Future of Travel Beyond the Stratosphere, by Willy Ley (Viking Press)
Never reprinted. Two available on eBay, one for $17, the other from $140. Not sure I'm going to drop even $17 on this.
* (winner) "The Science-Fiction Field", by Leigh Brackett (Writer's Digest, July 1944)
ISFDB lists printings in 2017 (unreasonably priced hardcover volume "Lorelei of the Red Mist: Planetary Romances") and in 2013 in a paperback called "Windy City Pulp Stories #13" which you can get on eBay for around $30. The original Writer's Digest issue is not available on eBay, nor on the Internet Archive.
* "The Works of H.P. Lovecraft: Suggestions for a Critical Appraisal", by Fritz Leiber (The Acolyte, Fall 1944)
Published in The Acolyte 8, which is at http://fanac.org/fanzines/Acolyte/Acolyte8-cv.html. You can also buy it in Fritz Leiber and H.P. Lovecraft: Writers of the Dark, paperback, for around $23 on eBay.
* Buck Rogers: "Hollow Planetoid", by Dick Calkins (National Newspaper Service)
You can read it online at https://ilovecomixarchive.app.box.com/s/u9qej2ihvt5xugyxzrr7jftf5sc62ao8/folder/110370933322?sortColumn=name&sortDirection=ASC.
* Donald Duck: "The Mad Chemist", by Carl Barks (Dell Comics)
Reprinted in the 1989 Donald Duck Adventures #15, which can be gotten for $6 or $7 on eBay, and probably cheaper if you rifle through stacks of old comics in a store (although you can't do that most places at the moment).
* Flash Gordon: "Battle for Tropica", by Alex Raymond (King Features Syndicate)
Available at a reasonable price in "Flash Gordon Volume #6 1943-1945: Triumph In Tropica" from Kitchen Sink Press
* Flash Gordon: "Triumph in Tropica", by Alex Raymond (King Features Syndicate)
Also in "Flash Gordon Volume #6 1943-1945: Triumph In Tropica".
* The Spirit: "For the Love of Clara Defoe", by Manly Wade Wellman, Lou Fine and Don Komisarow (Register and Tribune Syndicate)
Read it online (it's only 8 pages): https://comicbookplus.com/?dlid=21755
* (winner) Superman: "The Mysterious Mr. Mxyztplk", by Jerry Siegel and Joe Shuster (Detective Comics, Inc.)
https://dc.fandom.com/wiki/Superman_Vol_1_30 has a list of reprints, which are readily available.
* (winner, tie) The Canterville Ghost, screenplay by Edwin Harvey Blum from a story by Oscar Wilde, directed by Jules Dassin (Metro-Goldwyn-Mayer (MGM))
Trailer here: https://archive.org/details/TheCantervilleGhostTrailer1944. There's a DVD on eBay for $15. I'm unconvinced from the trailer that it's worth $15 to see. $7 if you have a working VCR.
* (winner, tie) The Curse of the Cat People, written by DeWitt Bodeen, directed by Gunther V. Fritsch and Robert Wise (RKO Radio Pictures)
Full movie at: https://archive.org/details/PhantasmagoriaTheater-TheCurseOfTheCatPeople1944970-2. Also available on DVD.
* Donovan's Brain, adapted by Robert L. Richards from a story by Curt Siodmak, producer, director and editor William Spier (CBS Radio Network)
This confused me, given that there was a movie adaptation in 1944, but called "The Lady and the Monster". Then I realized the nominated work is a radio drama. (Yeah, it says it right there: "CBS Radio Network", but I missed it.) It is here: https://archive.org/details/DonovansBrain1944 (both parts)
* House of Frankenstein, screenplay by Edward T. Lowe, Jr. from a story by Curt Siodmak, directed by Erle C. Kenton (Universal Pictures)
Trailer at: https://archive.org/details/HouseOfFrankensteintrailer. There's a DVD. Run ya $10 on eBay. Edited to add: Also available on DVD from Netflix.
* The Invisible Man's Revenge, written by Bertram Millhauser, directed by Ford Beebe (Universal Pictures)
Full movie at: https://archive.org/details/UniversalStudiosMonsters1944TheInvisibleMansRevenge. There's also a DVD for $19 and up on eBay.
* It Happened Tomorrow, screenplay and adaptation by Dudley Nichols and Rene Clair, directed by Rene Clair (Arnold Pressburger Films)
Full movie at: https://archive.org/details/ITHAPPENEDTOMORROW. DVD for $19+.
I don't know how to go about fairly evaluating the nominees
I don't know how to do this one either.
Read them all at http://fanac.org/fanzines/Retro_Hugos.html