once your in the navy in the submarine force as a striker can you pick
any rate in the navy even if it is not on a submarine?

Once you've volunteered for sub duty and have completed sub school,
you are commited to sub duty. You can only strike for a seaman rate
(non-nuclear) which is a crew position on your boat.

cvenom-ga's answer is generally correct, but I've seen at least two
sailors strike for rates outside subs; both had completed sub school,
and both were submarine qualified (had their dolphins).

The key to getting this (if it's what you want) is performance.  The
command has to give you a very positive endorsement, and justify why
you should be allowed to go outside the sub community when you are
already a submarine asset.  If you are a marginal or sub-standard
performer, the command isn't going to go out on a limb for you.  If
you are a stellar performer, and make a good case for it, it's
possible.

This does not preclude things like officer programs, by they way.

In general, once subs, always subs, but exceptions are made for hot
running sailors.  Also, if you qualify for a cricital rate, they may
take you over even if it's out of subs (if it's manning situation is
bad enough).