How long does it take to adjust to life overseas?

Will I always feel a bit lost, or out of place?

This is really up to you.  An old axiom says that  "A real person of the world - feels comfortable everywhere - but really at home nowhere." 

Adjustment is a real issue for many people.  The author feels most at home on Phuket Island, in Thailand and doesn't feel at home back in Arizona, in the USA.  But that is him - not you.

Adjusting

Some people never adjust, some people fit right in immediately.  Most are more middle of the road and need to make a few friends, get to know the lay of the land, learn where to shop, learn a few language basics, etc. before starting to feel comfortable.

Can this stage be a bit uncomfortable?

Of course!  But it doesn't usually take long.  A lot depends on how you view where you are living.  Do you look at it as a long-term home? A one-year visit?  A two-year party?  After the author had lived in Botswana, Korea, Taiwan, Saudi Arabia, and Bangkok, Thailand (from 1989 to 2002), he was desperate for a place to call home.  He wanted a cat, a house, a yard - all those familiar things from his "old" life.  Once on Phuket, he let out a big sigh - and knew this was home.

So . . .

Once you have wandered for a long time, you might find yourself seeking a place to put down some roots.   It will get rid of that edge of not belonging anywhere.