OK You need to find the part number on the IF can. Is it the first, or 2nd. IFT?
http://www.shortwaveradio.ch/lib/exe/fetch.php?media=manuals:hallicrafters_s-120.pdf
download JW miller catalog:
http://www.tubebooks.org/file_downloads/Miller_No-61_.pdf
Look up the IF can cross number.
Someone here may have one.
Yes, you will need to re-align the radio after replacing the damaged IFT. Above PDF has alignment instructions.
That being said, if the bakelite core is not damaged, you may be able to remove any damaged windings, CAREFULLY counting the turns- Write the number down! Then using a micrometer, determine the wire size you will need to replace the damaged wire with. Friends who have done this said they scramble wound the wire on the core (auto radio), and coated the winding with bees wax. Realigned, and I actually saw this and the radio working just fine. If the casing of the IFT is smashed, you will need to try to straighten it out & re-use it, unless you can find a replacement. The IFT does need to be shielded.
If JW Miller has a replacement you can find, typically they come with the metal shield.
The loopstick is an easy rewind job, and again bees wax to hold the windings in place, rewinding with same gauge wire. If the loopstick is broken, General Cement- GC Products actually makes a special ferrite cement for this purpose.
That all being said, that is a really common set and likely someone had a "hanger queen" kicking around for parts.
Of note is that Hallicrafters radios IFT's had a large number of failures due to the small capacitor in the base having silver migration disease. Even if the IFT you can find has this problem, it is a fairly easy fix. many previous posts here and elsewhere on the way to repair it.
Hope this helps. please let us know how you make out.
Also post here in the wanted section for the IFT when you figure out which one you need. Typical 1st & 2nd IFT's are not interchangeable.
Good repairing!