What leg muscle is responsible for my legs kicking strength and how can I improve this muscle effectively?

Answer 1

The whole leg. Jogging, and gym equipment that focuses on the legs.

Answer 2

Do the following:
Quadricep extensions
Hamstring Curls
Squats
Hip Abductors
Hip Adductors

Ive played soccer for years and the first and last two exercises really helped my leg strength when it came to kicking, but you dont want to overtrain any part of your legs more than another.

Answer 3

Do EXPLOSIVE movements. Squat JUMPS especially. Don't use machines. You will not use your stabilizers as well if you do. Try to find a core training class like pilates (I'm not kidding) or Hatha (power) yoga is even better.

Lunges are good. Hip abductor and adductor depending on the specific exercise can be great.

Answer 4

That would be your quads and your glutes-so squats and lunges.