Damn GetBig server, i wrote a full page response but it didn't send and then I lost it, so noe you get the condensed version.
First and foremost. Don't rely on the straps, use them only on your heaviest and hardest sets. If you rely on the straps, your grip strength will never grow. Use chalk, Chalk is good and get a solid "alternate grip" on the bar, (dominant hand over, and weaker hand under.) Some guys switch up the alternate grip every set just to even things out, but I have never had the need to.
Good secondary exercises for grip would be the "farmers walk" and "farmers hold".
Farmers walk: grab the heaviest set of dumbells you can handle, get your hand grip in deep under the handle, squeeze as hard as you can, slowly stand up and walk from one point to another, then turn around and walk back.
Farmers hold: use a power rack and set it so that the barbell is resting about 2 inches below your deadlift lockout point. Load the bar with 50-100 lbs more than your max deadlift. Then grip and hold for as long as you can. Using overhand grip, underhand grip, and alternate grip.
You can throw in 2 or 3 sets of these grip exercises at the end of your workout on deadlift day. Make sure it is at the end, because after doing these, your grip will be shot for the rest of the day. I particularly like the farmers walk. Walking gives you enough vibrations and instability that you really have to squeez hard to control the dumbell, I've also notices a good bit of forearm growth from both the farmers walk and farmers hold.