I need to remove a wall plug. There are 4 wires connected to the plug. Two are black (actually one is black and white and one is all black) which are connected to one side. Two are white connected to the other side. Then there is the ground wire. Is it proper to connect the two black together and two white together and the grounds together so I can put a cap plate over the hole?
Yes, that's probably fine. Assuming the tabs connecting the two screw terminals on each side of your outlet are intact, the outlet is being used both as a receptacle and to join those wires. Simply connect the wires (including grounds) directly using wire nuts and remove the outlet, then install a blank face plate. Make sure the location remains accessible, this is required by code for future service.
If the tabs (particularly the black/hot side) are not intact, then the outlet is likely partially switched. (This is a little more likely because you mentioned a black+white wire.) If you do find that it's a switched wire, then you should simply cap the black/black+white wires individually rather than bonding them, so you don't create a loop in the circuit.