generally these two phrases are close in meaning. A fine difference is, no more indicates amount and no longer indicates time. I have no more money left. I no longer stay in Bristol. But, often they are used like synonyms. Like in the previous example, "I'm not going to take your complaining any more( no more complaints)/any longer (not going to spend time listening to them) hope this helps. :)

They are very close. If you work at a store and run out of something, you could tell a customer, "There's no more of those left." However, you could also tell the customer, "We no longer have any of those." Both express the same meaning. If your pet dog dies and your child asks you what happened to it, you could say, "Sparky is no longer with us." Or, "Sparky is with us no more." If you're tired of someone's constant complaining, you could say, "I'm not going to take your complaining any more/any longer." Both work here. Hope that helps.

I like this song: can't fight this feeling anymore.http://www.youtube.com/watch?v=AI_k8mVqeLA&feature=related