Why was the League of Nations unable to prevent German and Italian aggression against other nations?
1.) The League wasn't designed to be able to do much.
2.) Britain and France didn't especially want to.
When the League was designed at the Versailles meeting, most nations, but France especially, didn't want it to have too much power. Remember they had just gotten out of a war caused by entangling alliances; it's not unreasonable for them to want to keep the international community out of each other's affairs for a while. France in particular, for example, opposed its having an army.
Britain and France were the most relevant nations to look to as far as enforcing the League's decisions, since they were the most powerful nations in Europe; both had signed the Treaty of Versailles, creating the League; and America was an ocean away.
However, they both pursued non-aggression policies at the time, because again, they had just gotten out of a war. So, when Italy invaded Ethiopia or Germany (basically) annexed Austria, they were content mostly to shake their heads and warn them not to do it again, because their main goal was to keep their soldiers away from fighting.