By priority moves I am assuming you mean offensive priority moves not including Fake-out(as that can only hit when you switch in). However if you do count Fake out all 3 Hitmons can learn it.
Hitmonlee and Hitmontop have: Vacuum-wave, Bullet-punch, Mach-punch, and Sucker-punch
Hitmonchan has: Vacuum-wave, Bullet-punch, and Mach-punch
Lucario has: Vacuum-wave, Quick-attack, Bullet-punch, and Extreme-speed
Scizor has: Bullet-punch, Quick-attack, and Vacuum-wave
So yeah these guys have the most Priority moves that I could find. So only Hitmontop/lee and Lucario can have a full set of priority(though Vacuum wave is not a very good move on the Hitmons and Quick-attack is redunant on Lucario because of Extreme speed). Ironically Hitmonchan can not learn Sucker-punch lol. If anyone knows of another Pokemon with 3-4 Priority moves please comment.
Note: I did not count Smeargle who is obvious.