I need to recharge my Axe of Whiterun (+10 dmg to health and stamina). I don have conjuration, is there any way to fill soul gems, or do I have to buy them?

Enchant a weapon with soul trap and you don't have to cast the spell.

I found a bow once with soul trap on it.... And damn.. I didn't know i had THAT many empty soul gems on me! like 100 soul gems in my inventory after a hunt ;P

That's what you should do! Find a soultrap enchanted weapon and wreak havoc!