I've got an old Sunbeam too. It has removable griddles that can be swapped for flat pan style. After I saw Robert's pictures I dug mine out and tried to use it. Big mistake. The oil on the griddle was rancid and smelled bad when heated. I sprayed it with PAM and gave it a go, the birds like waffles too, and ended up with a mess. The batter stuck to the top and bottom and ripped the waffles apart when I opened it. I pulled the waffle grids out and soaked them and gave them a good scrubbing, I haven't tried them yet.
Not sure how to proceed. I have an old aluminum griddle we use every week to fry pancakes and my dad is not the best clean up person. Over the years the bottom was coated in grease and oil and had blackened quite badly. Not to mention it was getting sticky. What I finally did was to put it out on my gas grill, covered it and the entire grill surface with foil and run it on high for 3,4, or 5 hours. (The Weber grill book states this is a way to clean the grill...) The heat buildup burned off the grease and a quick scrub with some Brillo did the job. I had thought about running it through a self cleaning cycle in my oven but opted for the grill as I can control that easier. I didn't think the heat would melt the aluminum but I didn't want to take a chance. Anyway that might be a good way to clean the waffle grids too, haven't needed to try it yet.
So, now I have them clean, How do I season them?