You have to be consistent and not break down and give him what he wants. Provide healthy food at meals and snack time. Start with giving him a small serving of a food he likes as well as food he doesn't like. Introduce the new foods, one at a time. i.e. Only one new food each week. Give him some of what he likes but not enough to fill him up. He will eat when he's hungry.
You have to get tough and not give in to him after you've said no. When you do that you're teaching him to misbehave to get what he wants. Bad, bad habit to get into and difficult to get out of it. You have to realize and accept that it's your responsibility to consistently teach him good behavior. Never give in. Yes, you will sometimes. Forgive yourself and start over.
He will eat when he's hungry. I suggest that although his tummy hurts he's still not hungry enough. Or......you've more consistently given in and he knows that if he just holds out you'll eventually give him what he wants.
Perhaps he will drink from a cup. 3 doesn't actually need a sippy cup. Let him drink water instead of V-8 juice which has a strong flavor. I understand him not wanting to drink it. Perhaps flavor the milk with a very small amount of chocolate syrup. Just enough to make it taste different but not so much he's getting too much sugar.
Give him mild, easy to eat foods as a transition diet. All the foods you mentioned are soft and require very little chewing. Chicken strips are more difficult to chew. Perhaps you could break them up into smaller pieces. Scrambled eggs are an example of another soft, mild food. All of you have scrambled eggs. Teach by example. Be patient.
My daughter has her kids eat just one bite of new foods. The next time she serves it, it's 2 bites, and on. Talk to him ahead of time about the food. Perhaps the first time he doesn't have to taste it but he has to have it on his plate. Then 1 bite, etc. She will also say we're having ice cream for desert. Eat 5 bites and you can have yours. Giving a choice, as mentioned by Momma L. sometimes helps. Having him help you choose and prepare the food might help.
If the high chair can be pulled up to the table without the tray, use it as a toddler chair. Otherwise put it away again. He's a big boy. Only feed him when he's at the table.
Eating can become a power struggle. Sounds like it's a battle already. So stop insisting that he eat. Be matter of fact. This is what we have to eat. We eat at the table. At such and such a time, we clear the table and put the food away. You can choose to eat or not. Then let it go. When he says he's hungry, offer him the nutritious food at the table.
If you can be calm and unemotional he will eat, eventually. He has to suffer the consequences of not eating before he will learn that he'd rather eat. When you get focused on making him eat the issue is clouded with control issues. When you're upset that he doesn't eat you your turn eating into an emotional issue.
You have to decide on the rules and enforce them in a calm and unemotional way. He won't starve. You will have days and perhaps weeks of him being cranky and complaining of a tummy ache. Eventually he will learn to eat what you give him.
This will take time. Don't set yourself up for failure by insisting that he eat new foods right away. Momma L. suggested that a child has to be exposed to a new food 10 times before they're willing to try it. So start out slow.
I suggest that a large part of what is going on is having to adjust to a new baby. I would still give him a bottle at night. Now, with a baby drinking a bottle, is not a good time to wean from a bottle. I'd tell him that during the day he's a big boy and big boys use a cup but that you understand how comforting a bottle is and he can have one at night. I'd then rock him with the bottle as a measure of comfort and so he doesn't feel totally displaced by this new baby.
I"d also spend time with him without the baby. Praise him for being a big boy. Have him help with the baby by fetching for you or even holding the bottle while you hold the baby. Talk, quietly with him about how the baby has no teeth and can't eat big boy food like he can.
He is afraid. Afraid the baby is pushing him out of his place with you. Unfortunately you're trying to make some major changes in his diet at the same time a new baby has made even larger changes.
Remember, it's no big deal if he eats or not. He will not go hungry for long. Be consistent. Be firm. Be kind, but don't give in.