Lots of reasons a boat can take on water. Too many to list. Water in the oil sounds like an engine problem: head gasket, cracked block, etc. Water in the bilge could be all kinds of stuff.
You have to see where it is coming in from. Best way to start is to put the plug in, and back it into the lake/river/ocean and look in the bilge. See if the water is coming in from one place or another. If it's not coming in with the engine off, start it up (if you can) and then see. Once you can see where it is coming in, you can narrow the guess work of why it's coming in.
Is the transom solid?