Some things, you dodge by running away from, and some things, you dodge by running towards. As a paladin, you should be handling most difficult situations by staying close to them, not by trying to stay away from them. Diablo’s red lightning attack looks like it’s originating at him, but it actually starts a few feet away from him. If you’re right up in his face, it won’t hit you. Of course, then his melee attacks will hit you, but such is life.
Disregard completely any advice from before 1.10. Thorns may once have worked well; it doesn’t any more. You should most likely be using the same aura against Diablo that you use against everything else. What aura that is will depend on your character type. If you’re focused on physical damage, you should be attacking with Zeal, and using Fanaticism for your aura (until you get Fanaticism, use Might or Concentration, but don’t bother putting more than one point into either). If you’re using Vengeance as your main attack, Conviction is the best choice. Or you could pump Holy Freeze or Holy Shock and synergies, and use that with Zeal.
Holy Freeze/Shock would be useful for single player, since the damage added by the aura doesn’t depend on what weapon you’re using, and as you say, you probably won’t have the best choice of weapons in single player. If you’re planning on going on to Nightmare and Hell difficulties, though, the Vengeance/Conviction route might be more useful. Since Vengeance does a mix of different damage types, it’s useful against monsters with any immunity, and in Hell difficulty, almost everything is immune to something or another.
As for your attack rating issues, dex really is a good way to boost your attack rating, in combination with your skills. Every point of dex will add four points of attack rating. Generally, with a paladin, you want enough dex so that, with Holy Shield active, you have 75% chance to block, and this will also usually be plenty for decent attack rating. You can also use Conviction, which lowers enemies’ resistances and defense. It won’t show on your character screen, but decreasing enemies’ defense is equivalent to raising your attack rating.
And don’t bother with Ancient’s Pledge. Really, about all it gives you is resistances, and you could get more resistances just by sticking diamonds in that shield (which is incidentally not a bad idea). Diamonds are especially not a bad idea if you’re planning on going on to Nightmare and Hell, where your resistances will be lowered across the board. I don’t know what runes you have available, but a Holy Thunder would probably be a decent weapon for a good while (certainly long enough to beat normal Baal), and worth using that socket quest on.
And don’t disparage the paladin. They are actually quite powerful, if used correctly, and by far the most versatile class in the game. They’re also pretty near indispensible, in a party, though that wouldn’t mean much in SP.