How do I clean deep burns in my oven?

So our apartment has an oven that, without fail, creates considerable smoke when we use it. And we've been trying to clean it as best we can with baking soda and vinegar, along with Bon Amie powder cleanser, but we can't get it to come out.

Here's what the inside looks like:

Other than hours upon hours of scrubbing, is there anything we haven't tried yet that we could do to get these burn stains out?