New freewheels can be had for around $10. Opening one up to clean and lube would be next to impossible (actually, only reassembly would be next to impossible). Just purchase a new freewheel (get one with the same number of cogs and with the same number of teeth on the cogs) and take the bike and freewheel to the bike DIY place, Should not take more than half an hour to swap out.

And if you really want to take it to the next level, take the old freewheel apart and see what you would have been in for trying to clean and lube.