Well, the first part of your results, and somewhat important is the load average. 1.83 is the 1 minute average, 3.65 is the 5 min, and 6.84 is a 15 minute average. This is showing average to slightly high loads (hard to really say for sure without knowing server hardware)
So.. the first clue is that the server may be slightly overworked. The second clue, is you see 300+ processes running. This is typical for a busy server.. not terribly alarming.
Next on the list is memory. as you can see, only 18436K is free, This isn't a lot. When you run low on memory, things need to be stored on the hard drive... which is the swap. Reading and writing data to a disk is much slower than to ram.
So, that is the jist of what that part you posted is. Again, nothing terribly alarming or really sticks out, it just seems to be a kinda busy server, which may be part of your slowdown. The one load average of almost 7 is kinda high, so if the server frequently spikes like that, that may be part of the problem. Or, it could be just the host not having MySQL optimized as well as they should, or a number of things
