Why does mixed oil water coming out of the breather of my cat pump 66dx?

Sounds like it could be a blown head gasket or a cracked water jacket I would advise draining oil and watching for signs of water in the oil secondly if you find no signs of oil in the water erase sale and out of pressure pump to the system if the problem can says if the problem continues as a temporary fix you can run a bottle of copper block sealer through engine remember though that it's only a temporary fix

You need to get the compression checked, there is oil getting into the cylinder, bad rings, valves, valve guides and valve seals can cause this....

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Plus,...if the bike has been sitting for a long time,it is possible to have water in the fuel tank. So i wouldnt rule out gas just yet. Most likely it is fuel mixing with oil,and the carbs are going to have to be taken off,cleaned,floats set,and synched. And of course,drain old fuel and replace with new fuel. It would also be a good time to change the plugs,and oil while your at it.

what you have is a bad seal or a crack within the pump crack more common if any water was left in it during the cold winter

Well if you feel there is exhaust being blocked then maybe the catalytic converter is plugged.
Where is the oil blowing out at? Exhaust??? A breather?
If you have oil coming out the exhaust then that could have baked in the cat and plugged it. But that would be the least of your problems as there should not be oil getting in there.
Out a breather or even a seal then it could be a bad PCV. But it still should not blow out much.

The rings or valve seals are letting the compressed fuel mix escape thereby pressurising the rest of the engine
The froth is old oil mixed with water - drain & flush engine

Yes there is another way, someone can be messing with your head and pouring water in your oil cap. Do have water in your oil or oil in your water or both? A product called sea foam does a miraculous job at getting water out of oil. As far as keeping it from happening further, the cheap way of course is "bar's stop leak" but man can this stuff do a number on clogging your heater core, even if they say it doesn't, it can happen.

stick your cok down the petrol hole

I had the same problem! I found that the needle valve in the carb was not shutting off the fuel flow when not running. Either replace needle valve or put a shut off valve in the fule line. Should take care of the problem