[cjm41]

Yeesh. Looks like you most likely need head gaskets providing that grey sludge is caused by coolant in your oil.

If that's the case, the engine doesn't need rebuilding necessarily, although it would be hard to tell if the diluted/watered down oil has caused any excessive wear to internals.

I'd get a second opinion on that grey sludge, and I wouldn't chance even starting the car again until you do.

EDIT:

Do an oil change first. If the oil looks fine it might just be oil and condensation accumulating around the filler cap.

If your oil looks milky/murky, all signs point to head gasket.