I literally don't remember anything about this except a specific scene where the wise companion keeps correctly guessing how many fingers the protagonist has behind his back.
Sounds like the 1992 cartoon series Mighty Max, an action adventure cartoon starring a boy named Max that had a magical cap that let him open portals to other locations. He was accompanied by a giant musclebound warrior named Norman, and a Lumerian "fowl" named Virgil, who looked much like an anthropomorphic owl or a chicken as they joked in the show.
In the season one episode, "Bring Me the Head of Mighty Max", according to Wikiquotes:
Max: Look, I already told you I am not going back down there! Besides, how do you know that's my destiny?
Virgil: Because I know almost everything.
Max: Oh yeah? Okay...who was the king of England in 1298?
Virgil: Edward the Second.
Max: Well, how many people are living right now in...Calcutta?
Virgil: Sixty seven million, nine hundred and eighty two thousand, seven hundred and thirty two...thirty three, sorry.
Max: Okay, well, uh... [He puts a hand behind his back.] How many fingers am I holding up behind my back?
[Max does a surprise take as he realizes that Virgil is correct.]
Your question suggests Mighty Max, except that was a series, not a movie. The burly warrior (named Norman, believe it or not) was the titular Max's protector while the owl-man Virgil advised Max when necessary (which was a lot). Max didn't so much travel to another world as go to different parts of earth though portals opened by his magic baseball cap (one did lead to outer space).