120mm steel frame...
 

Got a nice old '77 Trek TX300 steel frame, large 24" (60cm) for my son, who's longer of leg than I am.

Some meatball stuffed a Deore cassette hub in it, which is 135mm and has the frame stretched way more than I'm comfortable with. They didn't cold set the frame, so its just got to be spread by hand to get the wheel in (takes two people, one to hold the frame AND push the wheel in, the other to grab the stays and spread them), and its ugly, the stays are visibly bowed.

I'm thinking a 127 or at most a 130mm hub would be a much better setup here. I'd prefer to find a 127mm cassette hub but would settle for a 127mm freewheel hub. I've got a big black gap in my knowledge of 80s/90s road bike technology. What sort of hubs are out there? Is there such a thing as a 127mm cassette hub? or did cassettes start at 130mm ?

Shimano cassette rear hubs were common from the mid-80's onward, and the industry switched the standard for road frame rear hub spacing from 126 to 130 sometime around 1991 - when 8-speed drivetrains became common.
You can always remove or swap out some axle spacers and trim down the axle of most hubs to make it fit better. You'll need to re-dish the wheel to get the rim back to the centerline again.

With the wheel out how wide is the inside measurement of the frame?

the forcing may have knocked the frame out of symmetrical alignment.

then you have a choice, go to a good bike shop and have the rear end Cold set and re aligned
Dropout and derailleur tab alignment.. is important particularly for index click shifting

126 is good for 6 or 7 speed but that cassette type has been made obsolete by the incessant drive to sell people that more 'speeds' are better..

I have found Phil Wood's Freewheel hubs to never fail. the axle is very strong.
so the cassette benefit of not bending axles by shifting the wheel bearing to the right end of the freehub, becomes less important.
6 and 7 speed freewheels are still made.

FWIW Shimano uses a 10mm diameter by 1TPmm axle, you can get shorter axle, and a thinner left side spacer ,
to fit the wheel to the frame.

Yeah I would first determine what the resting width of the frame is.
I would probably go for a cold set to 130mm, get the frame/drop out and hanger alignment set on the rear and go with a newer 130mm wheel and 9s or 10s cassette. Unless you really just want to go old school. If you do go 126mm go with a freewheel setup on friction, they may be obsolete but I don't consider them as obsolete as a 126mm cassette would be.

A) the bike has friction shifters, old Shimano 600 downtube shifters. it has a 7 speed cassette now.
B) sadly, the bike has left town for a few months with my son who left for college, so I can't measure the inside spacing until he gets home for Thanksgiving. I only had two days to set things up for him as we got the bike late Monday PM and he left Thursday AM early.
C) 7 speeds is my goal. friction shifting 8 speeds or more is pain. I've already got a suitable 7-speed cassette.
D) I'm willing to do the cold set myself per Sheldon's instructions, and use the string method to check frame alignment, then take it to a LBS to tweak the dropout alignment (frame has forged suntour dropouts that look a lot like vintage campy ones).

so... 7-speed shimano road hubs from the late 80s are probably what I'm looking for? new phil wood stuff is just too expensive for this, we paid $220 for the whole bike, and I'd like to try and scrounge what I need to build up two new wheels for not more than about $200 total.

Old 80's hubs that are open ball bearings are not something I would base a wheel build around unless it was going on a collectible bike. Don't get me wrong, I rode in the 80's, my bikes are 80's but they didn't have good seals back then, if at all, and the amount of maintenance involved in keeping them running just isn't worth it to me. I would rather ride. Also 7s cassettes, while findable, aren't always easy to come across. That is why I recommended freewheel or newer cassette wheels. Now Sachs, Phil, Suntour, Specialized, and some others all made sealed bearing hubs in the 80's and you can find them on ebay easy enough. I have 2 sets of Sachs and 1 set of phil's in 40 hole design I picked up for not much money.
Another thing might be to get a newer cassette hub and space it for 7s/8s. At least that way, later on if he wanted he could move up to 9s/10s easily with new shifters. I am running Shimano 10s DT index shifters and they only cost 40 when found on on sale. Or you could find something like this and get a better rear hub now. If your willing to keep the DT shifters and not get STI's then you can build a nice indexed system for not a lot and still get good wheels.

I dunno, the campy hubs on my mid-70s touring bike are in fine condition. of course, thats mid 70s Campy NR for ya. heh.

as I understand it, 127mm hubs were 6-7 speed, while 8-9 road hubs are 130mm. I don't think I want to stretch this frame that wide, its stays are quite slender, hence my looking for a 7 speed hub. and there's really no problem finding new 7 speed cassettes, they are used on a wide range of 'hybrid' type bikes, Shimano has a whole set of gear ratios in their catalogs. OTOH, if the 7 speed hub was for uniglide, I'd have to replace the freehub part, which is doable on Shimano, but difficult on others.

anyways, now that I'm looking, I'm seeing some Shimano 105 127mm road hubs on fleabay, so i may go that way.

I'd wager there are plenty of nice 7-speed cassette wheels getting retired in your area by folks converting their old 80's bikes into SS/fixie's. The trick is finding a good one without too much hassle. Maybe a 'wheelset wanted' ad in you local CL?