I play Risk 2210 with my buddies pretty often. The moon makes for some interesting strategies. One of my friends is famous for losing all the major land battles and then running to the moon.
As far as strategies go. For classic risk, PATIENCE! Patience is key, i'm sure someone mentioned this.
For 2210, my strategy is to hold onto something small, but decent. I like North America best because for some reason, there's always a nuke zone on the country that links North America to Asia. Diplomacy is also important. If you're a decent country, ally with someone slightly stronger than you. When the time is good, backstab them
As for lotr risk, never played. But i'd love to try it.