In-game paralysis... what's the next step?

Hi folks, novice here. I'm playing a computer opponent on my phone who violates all of Rensch's rules (queen out early, redundant early moves) and still pounds me into the ground every time. This time, I tried to ignore the computer's antics, concentrate on development toward the center, and pair my rooks. I've now achieved what I think could be a strong position, but I have no idea how to exploit it. We've only exchanged a few pawns, so I don't know if trying to work toward mate is realistic here. On the other hand, I want to keep the computer under pressure. If anyone could help me with some strategy here, I'd appreciate your thoughts!

There are probably multiple plans. I have now one simple idea.

You can take Nxb6 if you remove Nd7. So 1. Nxc8 Rxc8 (or Qxc8), 2. Bxd7 Qxd7, 3. Nxb6 forking Queen and Rook. After exchanging I would try to attack a5 and move the qeenside pawns forward. For example 3... Qc7 4. Nxc8 Qxc8 and now Rxe5 as the f6 is pinned. a5 is attacked, so Qa8 or Qc7 and Qc5+ with check and getting the a5. I hope this all works as I'm doing this just in my head and my calculation skill has its limits. 

I would suggest to you to do the tactics puzzles. I'm trying to do at least 10 per day and on each tournament I can see more things. It's incredible, how horrible positions can be "fixed" with tactics as long as you see them.

Those are excellent suggestions--thanks for taking so much time to think it through! It seems the important message is to focus on gaining material advantage rather than fixating on possible mating tactics too early. I'm noting that I tend to rush, because I'm worried about the adequacy of my defense. As you rightly suggest, more practice is in order!

Actually, you are always solving a very concrete position. Sometimes you can solve it with a tactic, sometimes you have  just to improve your pieces. As you learn more concepts, you get more tools. With more tools and more dexterity the harder tasks become attainable.