Do you give him the junkfood he wants?
What do you do when he won't eat what you make for dinner?
Are you a single parent? Where is the dad? How does he interact with him?
Any siblings? if so, what kind of relationship do they have?
Has he always behaved this way?
His father not enforcing rules could be a huge part of the problem. You can write down a list of rules and make an agreement between the two of you to stick with it.
Overall, children want attention, if children do not get positive attention, they will take negative attention. They want to be seen, noticed and loved. As for the eating, you cannot reinforce negative behavior with a reward, you already realize that. He should be old enough to understand cause and effect. If he can understand what you are saying to him when he's talking to you, then he will understand that when he does the wrong thing, he will be punished. Whether it's time out, losing a toy, losing a desert or snack, going to bed early, etc. You want to build a sense of responsibility into him since he is the older child. Tell him he's mommy's 'big boy', mommy's 'helper'. When he does good, be sure to praise him, since he is a little older, give him something a little extra sometimes, whether it's letting him stay up 15 min later than the other, or getting something that's only for the 'big boy'. Praise him for watching his little sibling and letting you know if they get into anything, praise him for not hitting his sibling, praise him for helping out when he does, etc.
Rules and schedule is what children respond best to. If there are no rules, schedule, or punishment, children feel like the world is out of control and they get fearful and tend to act out. Create a daily schedule and make him stick to it. For example, if bedtime is 8pm, then at 7:30, announce the time, and what you are about to do ('it's 7:30, pajama time!'), read a story, turn out the lights (maybe have on a night light and soft music, not tv at bedtime) and every night, try to do everything the exact same way.
When it comes to rules, since he can't read you can make a poster using pictures. No jumping, no screaming, no hitting, etc. Draw pictures to show jumping, hitting screaming or to describe whatever behavior you want him to stop. Go over the poster with him every day, and what the punishment is if the rules are broken (no tv, no toy, no desert, etc). No second chances, each time the same thing should happen. He has to realize that what mommy says goes. It may seem hard or harsh, but I guarantee you that it will hurt you far more than it will hurt him, in fact he will feel more secure, safer and happier overall knowing that you are in charge and not him.
Be careful of the cartoons he watches, there's nothing wrong with not letting them watch them. He should also not watch any moves except movies that are rated G. I tend to steer away from tv completely, especially because of the commercials, and instead bought a dvd player (put it up out of reach) and started a collection of children's DVD's. No tv or radio at all except for cd's and dvd's that are age appropriate.
There's nothing wrong with giving him the choice to eat one or two things at the dinner table, but to let him spit it out, or to make him something completely different is asking for trouble. Either he eats with the family, sitting down, behaving, or he goes to bed. It might seem harsh, but you would be surprised how quickly he catches on that his behavior is unwarranted.
I welcome your thoughts, let me know if you want to talk more
Undermining your authority and disrespecting you in front of the child is likely exactly why your son is acting out. This is something you will have to address with the father and if it means limiting his time, or even hiring a babysitter until the father can get it together. I know the decisions are not easy when you feel like you don't have a lot of options, but when you honestly feel like you know what the problem is, that's a good start, you just have to figure out how to move on from there.
I'm here if you want to talk more
I'm so happy to hear that from you. Yes! Children prefer positive attention, but if something else is bothering them, they don't care if you're screaming at them, they know that at that moment they have your undivided attention. Also, consistent, consistent, consistent. If you do things the same, keep your rules and punishments the same, and his schedule the same (I know sometimes it's not possible, but as much as possible) then you will notice a much happier, content and calm child.
Feel free to ask for me by name anytime you want to talk, I'm always here to help you.