skyray, to give you specific tips, I'd have to see some recordings of your games. That being said, generally speaking you should arrange your navy so that battleships are up front, carriers right behind the battleships, and subs behind the carriers. At defcon 3, launch all carrier-based bombers parallel to the line of battle. If you see the enemy, start maneuvering around him (I like to back off if I see him charging in, gives me more time to engage). As for your subs, don't blind fire them, don't try to sneak them around. Surround them with your navy (again, battleships up front, carriers in the rear). Spam fighters in all directions (or at least the directions of likely inbound bombers). Synch your shots as well. Every first shot from the subs should go to target A, every second shot to target B and so on.
Using your fleet defensively is a bit advanced. You need to learn how to naval nuke properly, and you have to be in constant motion. And you have to accept that perfect defense in this game is nearly impossible, the defensive posture is really just a speed bump, not a wall, in the face of a determined and experienced attacker.
From your description of a close range engagement, it sounds to me like you're not getting your bombers up. Don't rely on fighter spam alone to win naval battles.
Also, get yourself a copy of this
, and watch some recordings of games found here
. Pay special attention to games in which Battletron, R3D, Ace Rimmer, hooru, Baton, CZA, Byron or Tobias are present (random sampling of good players, no offense intended to anyone included or left out). Watch how those guys use their navies, and try to emulate it.
Finally, the AI has no advantages at all. In fact, the AI is terrible and predictable. If you can't beat the AI, you can't beat any human player. There's a few schools of thought on how to fix your particular problem (inexperience) but they all boil down to "practice more".