From IvanWiki

Higher Leg Strength lets you carry a heavier pack, and increases kick damage.

Carrying a heavy pack until you are Burdened or Stressed naturally trains your leg strength. Kicking things trains your leg strength also. Drinking Ommel Urine also raises Leg and Arm Strength

Instantly increase LStr with prosthetics (lose a limb and pray or use a Scroll Of Change Material on a limb)