IA-32 = "32-bit Intel Architecture for x86."
IA-64 = "64-bit Intel Architecture", but is an entirely different ISA (Instruction Set Architecture), and even uses a radically different processing paradigm.
x86-64 = "AMD's 64-bit extension of IA-32" Basically the same type of straight-foward extension that was made by Intel going from the 286 to the 386. There are other differences of course, but this is a summarization
Pentium 4 is intels "7th" generation architecture, thus would be something like a 786.
x87 refers to the floating point capabilities of an x86 processor.
EDIT:
When I say "radically different processing paradigm" I don't mean that it doesn't use the Von Neuman processing paradigm, as it does...I'm just saying that it takes another approach than x86 and other current CPUs