Do these numbers have any sort of claim to MHz or are they just arbitrary numbering systems by the chip manufacturers?

Just numbering system. That's all.
Has nothing to do with CPU speeds whatsoever.
E7200 (2.53GHz), E8400 (3.0GHz), and Phenom 9950 (2.6GHz).

generally the first number is the series of processors, i.e. e8xxx, which tells you stuff like manufacturing process, cache size, fsb (usually but not always).
the last three numbers indicate the relative clock speed within that series.
so all the e8xxx processors are physically the same, but the e8400 has a higher clock than the e8200 etc.

Core 2 Duo E7200 is a 45nm chip, 2.53GHz with 3mb L2 Cache, and E8400 is a 45nm 3.0GHz with 6mb L2 Cache... Phenom 9950 is supposed to be 2.6GHz 4x512kb L2 + 2mb L3 I believe.

The numbers are mostly meaningless other than the first number denotes the series (E7xxx), and the second denotes their speed compared to the other models in their series.

Lol, what they said.

oh, and the E = dual core and if you get a Q that = quad, for intel, and for phenom its the number next to the X (eg X4 for a quad, X2 for dual)