Carb cleaner should loosen / dissolve the carbon and gunk, but might dis-color the aluminum. New stuff is not the same as what we used to get - it's " Enviro-safe". I remember leaving a Quadra-Jet in the little metal pail / basket carb cleaner you could buy at the auto store- I forgot it for about a month and all there was in the basket was some grey goo and shiny brass parts- the thing had dissolved.
 
Anti-freeze in a crock pot will clean it also. I put the anti-freeze in a small can covered with tin foil and put the can in the empty crock pot to heat up. Slow cook it on high overnight and it should come out nice and clean.

Don't know about oven cleaner - but most are caustic and will stain stuff.

Make sure the anti-freeze is for aluminum engines.  DOC Holliday

On the subject of brushes.. you are going to want a stiff one... I use a brush that is nylon and super stiff .. I have no idea where I got it.. I suspect Harbor Freight carries the black ones.. a tooth brush will work but use a new one if you can..

Also if you don't have a basket you can use a pieces of copper wire or coat hangers attached to the parts .. be careful of the piston and liner.. that's it..

When done.. you can save the anti freeze for the next time by Duct Taping the lid on.. store where it won't get knocked over..

I picked up my Crockpot (new) for $2.00 at a Church Rummage Sale.. 

Carb Cleaner will work... but wear safety glasses this stuff doesn't feel good when it gets in your eyes.. don't ask me how I know? 

Jim