These phrases come from a formal dictionary definition of "meet".
I would not call them fixed phrases and they are not ones you will commonly hear in general conversation.
As for that they mean, I would say "come into the presence of" means to come into the same room as someone but not necessary talk to them. You might use it when coming into the presence of a very important person.
"Come into the company of" is less common, and I suppose it is joining socially rather than just being in the same room.