I'm sure he or she will encounter them in the end.
Probably, but at the same time I don't think Marvel needs to have the attitude that every single movie they make has to be a part of the same universe and connect up in someway. Eventually that will just get to difficult to manage. Right now they've got a pretty good set-up with Cap, Iron Man, and Thor solo movies with the potential of adding a Hulk or Black Widow franchise. Adding more solo franchises that are also meant to tie into Avengers in someway seems like too much.
But if it is just some solo character not currently introduced but meant to tie-in to the Avengers in someway, then Ant-Man probably makes the most sense.
As for how to make Dr. Strange fit into the current Marvel Movie Universe...just make him a guy who, for some reason, has knowledge of the super advanced "science" aka magic of places like Asgard. Doesn't seem like it's that big of a stretch. I feel like people are overthinking it right now. If you get a good creative team and cast involved I'm sure it could work just fine however they decide to do it.