Hi S.,
I have found that some kids are smarter and, if you can stomach the term, more manipulative, even at 2 years old, than others. He is either really working you over (my daughter was a master, and is still really good at this) or, he is having bad dreams. I have 3 ideas for you to consider. I have done them all...
It seems to me like he knows a lot of characters from children's movies. He knows them well enough to act out their personalities. While this is amazingly creative, it also suggests he watches tv, movies etc a lot. Try getting him outside, a lot, running his little legs off until he's completely exhausted. Make these days incredibly fun and something to really look forward to. Invite kids just a couple of months older than him to be a part of this too (with their moms) Play with the kids while they're out there...be a part of it with him.
Also, watch his diet. Make sure he is not getting too many starches (breads, pastas, crackers, cookies etc...) or sugars. My daughter reacted pretty violently (personality wise) when she had much of these food products. Substitute peanut butter celery, carrots and other fun finger foods...
Now, for the stay at home dad part: Is the day structured for the kids and him? He would do very well, for both kids, to run the day like a day care would. A time for reading, a time for coloring and puzzles, a time for playing outside, a snack time, a specific time schedule for all things done throughout the day. Make sure it's "productive" for the kids. This will implement, in the little, one that time lines are safe, normal and good because he will know what to expect. This was the most beneficial thing I put into place with my daughter. She began sleeping regularly and without dramatics, she ate on time, she picked up toys on time and so on. We were all much more calm and much happier. It took about a week or maybe 2 for this plan to completely ease the distress in our lives. Kids need specific boundaries to feel safe. They appear, at first, to hate them sometimes, but they thrive with them!
Good Luck!