My son (now 8) went through a picky eating state early on. Our strategy was to not make a fuss about it, but also to not cave in and serve special stuff. We made dinner, which may have included items he "didn't like" or refused to eat. Any whining was mostly dealt with by saying that this is what's for dinner, it's the food on your plate, eat it or don't eat it, but there certainly doesn't need to be any freaking out about it. We didn't make any special food just for him, and other than a rule of trying one bite of everything served, if he didn't eat a certain thing on his plate, or didn't eat anything else, that was fine.
The reality, I find, is that kids will eat when they're hungry. Maybe he's trying to push boundaries for awhile, maybe he's going through a stage or phase where he just isn't intersted in eating or isn't feeling hungry. If your pediatrician says he's healthy, I would just let it go. Offer him nutritious items for snacks and meals, but don't get into a battle over it; that will just escalate the issue into being about who can 'win' the battle - we all know that 4-year olds can be irrationally stubborn! When he's hungry, he'll eat, no matter what you're serving.
Any melt-downs or tantrums should be sent away from the table, I think. Emotions are great and I encourage them, but the family table isn't the place. If he's upset, have him get down and go to his room - not as a punishment, but just as a "hey sweetie, it's okay to be upset, but you need to take it to your room. When you're feeling better, come on back".
I believe that kids are just little bundles of feelings and thoughts and opinions and emotions and they're learning every day to sort through them and figure out who they are. It's our job as parents to provide boundaries, so they feel safe and can clearly see where those limits are and work on keeping themselves within them. Consistency and maintaining your own even, understanding tone is the key! :)