There are a couple of things I notice right off-you said "He seems constantly cranky and rubs his eyes a lot throughout the day, and yet when nap time comes he fights it with a fury' You have got a baby that is stuck in a constant over-tired mode. Not napping, going to bed way late are creating this problem. Babies who are over-tired will run wild. They get wired when they are over-tired.
When you note the first signs of being tired you take him in for nap. When little ones get over-tired they get wired and can not calm down and unwind for sleep. You have to break this cycle and it is going to take time and patience given that you are dealing with a toddler.
You need to literally do and say the same things for every nap and every bed time. It will take time but he will learn what is expected and what to expect. Babies have to be taught to sleep. They don't just know how. At 15 months he needs to be in bed waaaay earlier than 9 or 10 at night. Try to get him in bed by 7:30. Start the bedtime routine with dinner time. Keep things consistent with what you do and say. This is going to take time. It won't be corrected in a day or even a week but he will get it if you stick to it. You can also check out Dr. Sears sleep book for toddlers.
My son was a wild child as well. But we went to the library every week for storytime (I took his drink and a snack and that's how I got him to sit for the story.) Your son is young so you can't expect him to sit for the entire time but at least a few minutes. We also did things like mommy & me gymnastics or music class. It was very taxing on me in the beginning but it made a huge difference in his behavior. My son was a bit over 2 when we started these activities.
**Edited to add:
I missed the part about him screeching at you. Try teaching him sign language! It is amazing to watch. I've been signing with my daughter since she was 8 or 9 months old and it is truly amazing how much she uses it. The Signing Time series is great but any sign we don't know we just look up on line and start using it. Funny thing too is once my daughter would start using the sign she would also use the word!