What would cause a 2000 Chevy Astro to drop in oil pressure and produce a 'popping' sound when accelerating - yet not trigger a 'check engine' light?

Not 100% on this but I would pull the plugs and compare them to [http://www.hioutput.com/tech/plug.html These Images].
But it sounds like your van is misfiring and the lose of oil pressure could indicate several things like worn bores/piston rings or valve guides. Good Luck and Remember.
Change Your Mind, Not Your Oil.
Use the First In Synthetic Motor Oil's.
See My Bio For more information.