How do you remove the oil cooler off a 500efi to clean it?

Remove both hoses from the ends. Remove the oil lines (hold the cooler fitting with a wrench and turn the hose fitting with another). Then remove the nuts holding the cooler to the studs that go through the bellhousing.

If you just want to flush out the water section of the cooler, then just take off the end caps. You can see right through it and won't have to deal with loosing oil and making a mess disconnecting the oil lines.
Eddie