While you can be on one team of each type, at the end of each week you'll only gain points from the team that earned the most points that week. However, note that given equal rating, 5v5 teams earn more points per week than 3v3 (88%), which earn more than 2v2 (76%).
To clarify with an example:
Let's say you're on three teams (one of each format).
And at the end of the week, each of the teams you're on has a 1500 rating.
Assume that you were an active player on each team (i.e. your team played at least 10 battles and you participated in at least 30% of each teams battles)
Equation for Arena Points calculation: