Birds do feel with their tongues and beaks - it's a third hand, if you will. They'll explore different things and use their tongues to determine textures of objects they're curious about. Sometimes beaking is purely exploratory and they only bite down hard because they don't realize that certain objects - such as your flesh - should only ever be beaked with a certain amount of pressure.
A large part of that comes down to training. You can opt to give a response, which I personally do (I never see my Ringneck quietly sit there and take it when my conure start aggressively pursuing him or biting his feet and vice versa). If my Ringneck bites with too much pressure, I will shake my hand lightly to encourage a release and say, "Ouch! No bite, that hurts, don't do that". Then I'll remove him from my hand. It's natural for any animal to remove themselves from a painful situation and to let the instigator know that it hurts. The important thing while doing this, though, is that your bird knows he can trust your hand. If your bird doesn't realize your hand won't hurt him and that quick movements from it or sudden shakes don't mean impending doom, then they may be quick to react and bite ever harder.
What I would work on first is rewarding your birds for positively interacting with your hands. That can be as simple as asking them to step up onto your open palm while they eat out of it and saying, "Good bird", or could be working on thresholds and rewarding them for letting your hands get closer and closer without them freaking out. I taught both my birds to accept my hand coming from above them in attempt to break their prey fears. I had my hand above them for about a foot, rewarded when they didn't move, and continued lowering and lowering until they became comfortable with my raising my hands over their heads and placing it on their bodies.
You can also encourage positive hand interactions by doing target training, which I recommend reading up on. You can work to target train a bird onto your hand, then reward, then work on station training. Eventually your bird will learn that perching on your hand and being there IS a reward in and of itself, but that takes time, patience, and lots of positive reinforcement.