Vintage whammy weirdness

is it the right arm? sounds like either the wrong arm or the threads are worn. but its weird to have it just drop all the way in like that

 

Sounds like you have stripped the thread in the block.

What kind of Strat? Anything other than a US model most likely has an alloy block (even the current Highway 1s do, as did mid-to-late 70s US Fenders) which is too soft and often do this.

There are only three solutions - replace the block (if it isn't a good quality one you may as well upgrade to something like a Callaham while you're at it); tap it out for a larger diameter thread (eg M6) and replace the arm to match; or have it drilled out and a threaded insert fitted (brass or steel) - this is quite a tricky job and only worth it on a 70s Strat you want to keep original IMO.

BTW, one major cause of stripped threads is constantly taking the arm out to put the guitar away. Don't - the whole point of the angled hole is so you can swing the arm round over the body and put the guitar in its case without removing the arm. Leo Fender designed it like that on purpose. But many cheaper modern Strats have a vertical arm hole so you can't do that, and of course they tend to have soft alloy blocks too...