You can use it in a self-cleaning oven. The risk/problem you may encounter is the chemicals will burn out your electricals and pilot. So you will have to be careful when spraying so you don't get it into any hardware. Afer you wipe out the stuff, follow up a couple of times with just plain water.
There are some non-aerosol versions of oven cleaner, but they're kind of hard to find. Easy Off made these sponges that released cleaning foam when you squeeze them directly on a surface.
I had an oven like what you describe. The people who owned our house before us, left a self-cleaning oven in some pretty rough shape. Like you, the smoke was too toxic, so I used oven cleaner. The oven was so dirty, all the oven cleaner could really do is get the first layers of goook off the walls etc. Once I got as much off as I could, I then used the self-cleaning option.
The smoke was better. But only a little bit, because it smelled like oven cleaner instead dead rodents like before.
After I got the inside presentable, I just wound up trading it in and buying a new one. The oven never really smelled right, even after cleaning it.
It was pretty embarrassing when we had guests for dinner. It was so bad, people would actually say it smelled like something died. UGH!