When does oddish learn a leaf move?

Answer 1

Oddish cannot learn a "Leaf" move; you are probably referring to the type "Grass". If you are, you can look at the list below. This information is only accurate to Generation V.

By leveling up, Oddish learns the following Grass type moves:

Absorb at Level 1

Stun Spore at Level 15

Sleep Powder at Level 17

Mega Drain at Level 21

Giga Drainat Level 37

Petal Dance at Level 41

Regardless of level, Oddish learns the following Grass type moves by TM Learning:

TM22, SolarBeam

TM53, Energy Ball

TM86, Grass Knot

Also regardless of level, Oddish learns the following Grass type moves as Egg Moves:

Ingrain

Father: Tangela, Tangrowth, Sunkern, Sunflora, Roselia, Roserade, Cacnea, Cacturne, Carnivine, Snover, Abomasnow, Maractus, Foongus, Amoonguss, Ferroseed, and Ferrothorn.

Razor Leaf

Father: Bulbasaur, Ivysaur, Venusaur, Bellsprout, Weepinbell, Victreebel, Chikorita, Bayleef, Meganium, Sunkern, Sunflora, Nuzleaf, Shiftry, Tropius, Turtwig, Grotle, Torterra, Snover, Abomasnow, Cottonee, and Whimsicott.

Synthesis

Father: Bulbasaur, Ivysaur, Venusaur, Chikorita, Bayleef, Meganium, Hoppip, Skiploom, Jumpluff, Sunkern, Sunflora, Seedot, Nuzleaf, Shiftry, Roselia, Roserade, Tropius, Turtwig, Grotle, Torterra, Maractus, Foongus, and Amoonguss