Hungry and tired preschoolers are always a nightmare. That's why we work so hard to make sure they get adequate amounts of both. (Honestly, I'm not at my best when I don't eat or rest enough, either!)
You wrote that he's almost 3. That's also not uncommon for 2s, 3s and 4s to try to assert some independence/control. And, let's face it--whether they eat, drink or poop is something we adults really can't control, though we try. Aside from this being the typical terrible 2 rebellion, let's make sure there's nothing else going on and try to figure out the food issue.
You have gotten some very good responses. I have a very picky eater, also, so I feel your pain. First, like others have said, rule out any underlying medical conditions like gum disease or cavities. A child who has an inner ear disorder also loses his appetite. Reflux and/or constipation? Also, there are some diseases, like sensory integration disorders, for some children who have trouble with food textures. I would ask if the eating problems are happening at just home mealtime or is it happening everywhere--in preschool, visits to relatives, restaurants? Time of day? I'd probably keep a journal to see if there's a pattern, which is something your pediatrician will probably ask. Or, he really might not be hungry. Measure his intake, output, and times to see if there is a pattern. Also, how much water or juice is he getting? He could be filling up on juices and water throughout the day. Honestly, if he's not eating anything, he'd be seriously ill by now. So, he has to be eating more than hotdogs to survive 3 years. What has his pediatrician said? When I was concerned about my babies' diet, the pediatrician wasn't. Go figure.
You wrote that the tantrums are worse when he hasn't eaten, but is he generally a strong-willed child in all matters? Is he like this at school? What is his preschool teacher or grandparent or any other adult saying about his overall behavior? If he's strong-willed across the board, we have a heart condition and possibly a developmental matter that might require some professional help. Of course, you will continue to parent your son by teaching/modeling appropriate behavior. You and your husband should develop a discipline/behavior chart of consequences the two of you will implement and follow-through on so you don't have to feel out of control when he's out of control. So, when he won't eat, we'll ____. When he tantrums, we'll send him to his room or the naughty mat. A great book for this is "1-2-3 Magic" by Dr. Thomas Phelan. Not every behavior warrants corporal punishment (spanking), and there are other ways to teach a preschooler appropriate behavior. Typically, if there is a behavioral problem, it's across the board and not just at home.
Another suggestion to help him with eat, include him in the mealtime prep plan. Is there a structure that gives him a sense of predictability? Is dinner a set time with a routine that includes him, maybe putting down napkins. He can help mix a bowl of salad or maybe some type of sauce for the spaghetti. If he's included, maybe he'll be more inclined to taste what "he" cooked. Worth a try. And, preschoolers still like bite-sized, small portions. He might prefer foods that look fun or silly, like a silver-dollar sized pancake with strawberry slices or cherries for eyes and a banana chip for a mouth?
And, to be on the safe side, until tested for allergies, you might want to try gluten free pancake mix, noodles and rices and organic sauces. Blueberry sauce or real maple syrup instead of Mrs. Butterworths. Also, try making a game out of the fruits and veggies. Test his knowledge of colors by putting different veggie and fruit slices on the table. And, if you're all eating together and trying the different dishes with dips and such, maybe he'll enjoy that.
Final thought, takes a little while though, there's something to be said about positive peer pressure. When we have fellowships at home, I'll put out a different food, appetizer and dip. My picky eater is more likely to try a dish with her friends present than when it's just the family.
If he's still resistant and his behavior goes south, you have to stay calm and remind him that he's probably tired and hungry. Try not to lose it. It's going to be hard because no one likes sitting with a screaming, out of control child, but just know that there are times when there is short-term pain for a long-term benefit. If you and your husband are consistent in your plan, stay calm and help him transition from toddler to preschooler, you should survive.