2004 f250 blowing blue smoke out the tail pipe and losing power

Read about the fault code at the link, but the answer about the relation to the smoke is no it will not cause that. P0320 OBD II Trouble Code Ignition Distributor Engine Speed Input Circuit...

Blow head gasket. Just did one today.

Could be head gasket, piston, or other nasty issue. Smoke isn't a good sign. Run a compression check, that may help indicate where the problem is.

Does the smoke smell sweet? That indicates leaking coolant into the engine

White smoke for a diesel means air in the fuel system. You will have to start at the engine, I start at the line going to the fuel pump. Get some fuel in a can, remove the line to the supply side of the pump and put another line from the can to the pump. If it starts and doesn't smoke , then you have to work your way back to the tank and find the spot that is sucking air. If it doesn't start the I would replace the filter first, check again. There is a possibility that the injector pump is bad, but these don't usually throw white smoke. They just make the engine have very little power or no start.

Hello white smoke is usually engine antifreeze,Blue smoke oil burning,Black smoke car running to rich on gas,gas is not burning properly.

Blue --is Oil
White- is Coolant

Bad intake gasket or head basket

sounds like its burning oil poss valve guide oil seals or piston rings also check there is no oil going through the air pipes to the turbo

You may have a blown piston ring, valve seals, valve guides, cracked head gasket or a cracked block, etc... It sounds major though for you to lose power suddenly and have all that smoke...

look for block return lines- air leak in suction lines -block fuel line or filter - defective injection pump -inoperative glow plugs.