Straps work really well! The only problem is that they can become a crutch and prevent your grip strength from improving. I've heard chalk is a good option. I've never actually tried it and know that a lot of gyms dont allow it.
you need to beef up the forearms, fuck all the straps and other bells and whistles. Get huige forearms and your grip won't slip. I have used chalk before during extremely heavy lifts but I wouldn't get into the habbit of using it all the time. Forearms, forearms, forearms!!!
I always use over/under, I can't do shrugs or deads with over/over (pronated) without pulling off the weight. I also try to switch up hands between sets, but my left is still the lagging one towards the last rep or two.
i wont use straps for deadlifts but I do for shrugs. I find that i get a better work out in the traps if both hands are pronated than over under but I dont like the feeling of straps for deadlift so I do use over under there and just alternate which had is over and whichis under everyother set. As far as how to get a better grip work your forearms like stated above and try some of the towel pull ups that are listed around here somewhere
IMO straps are good to use during deadlifts, if and only if you do something to train your forearm and grip strength. You do not want to stop your set short while deadlifting because of forearm or grip strenght, so that is why straps are valuable. As I said do another exercise for forearms and grip.
Grant I think your thoughts are legit. And in your case I would use them but like I said what needs to be the determining factor is if your grip is hindering your lifting the most weight you can effectively, like it is for me doing shrugs, then you should use them. Just train forearms more like Grant and other have said. Deadlifts for me are limited by my legs (which is pretty embarrassing) and the right side of my lower back