Many throw traps and tick throw attempts can be escaped by counter-throwing. DeeJay has the benefit of having 4 throw buttons, which you can drum your fingers on to get many rapid throw inputs, similar to doing a piano reversal. One thing to watch, though, is throw ranges (can be viewed on this page: http://nki.combovideos.com/data.html). It is possible for some characters to simply out-range you…throw you from farther away than you can throw them. Fortunately, this isn’t really the case for Ken or Balrog, so you can counter-throw them fairly reliably. And since reversal throws get priority, so you’ll usually win the exchange.
Blanka, on the other hand, can fairly easily outrange DeeJay’s throw, which makes him more of a challenge. Basically, you can’t let him jump in on you…ever…or he will bite your face. This means trying to maintain a down charge pretty much the whole game, and being on-edge, ready to upkick any jump ins. And if you get caught without a charge, and he jumps, try to anti-air him however you can (s.strong, probably), because even if it trades in his favor, you’re saving yourself a throw’s worth of damage. Also, if you do get caught in a bite, shake out of it by mashing the buttons and moving the stick back and forth from down-forward to down-back, so you maintain your down charge, and can be ready to upkick again as soon as you escape.
Also, as 1hitparry said, reversal upkicks can be another great way of escaping. The short version has a lot of invulnerability and recovers quickly, but the stronger versions hit faster (for anti-safe-jump) and travel farther, so any strength can be a useful escape tool.
For Claw wall-jumps, there are a few things that work reasonably well. If they take a pretty basic trajectory, or even go a bit behind you, s.strong, or late short upkicks work most of the time, and put you in a position to apply some pressure. If you can guess when and where they will be, j.roundhouse is probably the most damage you can get out of it, but will sometimes trade if they extend their claws early in the dive. For a catch-all, jump back j.short seems to work pretty much all the time, but doesn’t give you a lot of damage.