My team:

Bulbasaur (Basic, Grass)
Parasect (Final, Grass/Bug)
Arbok (Final, Poison)

Bulbasaur V. Staryu: Grass Beats Water. Pokemon 101 right there, Bulbasaur wins.

Arbok V. Psyduck: Arbok is Final, Psyduck is not, Psyduck is snake food. Arbok wins.

Parasect V. Starmie: Parasect is Grass, Starmie is Water, Parasect is Bug, Starmie is Psychic, they're both final...Parasect wins handily.

Result: V I C T O R Y !