Will the early 2008 MacPro dual 2.8 GHz quad core function with the newer Intel 4GHz chips? If so, which ones?
Nope! As Intel releases new processors, they also release new processor sockets, so the new processors, besides not being supported by the computer, literally won't fit in the computer.
The highest upgrade you'll be able to do is something from the same product line. The highest processor in that line is the X5492, which clocks in at 3.40 GHz. According to this Apple forum, these processors will work, although your fan speed may increase.
If you have never replaced a CPU before, ask someone who has for help and watch some tutorial videos, or take it in to somewhere to get it done for you. As someone who recently completed their first processor replacement, I can testify that forums and videos will be essential to a successful upgrade. Good luck!