Currently used are Thunderbolt, Quick Attack, Iron Tail, and Electro Ball. The anime generally follows the games in just having four moves at a time available but they've never really given reason why that happens.

As for the number of moves he's actually used, barring improvised moves/combo attacks and also moves he actually shouldn't know and i'm not going to keep, it's 9, four of them electric-type and one the others is just a stat-booster.