My DD1 was hellish with food and as she was so dinky I pandered to her, she quickly realised that food and mealtimes were a great opportunity to gain control (which is entirely normal and a part of childhood development, but needs managing!)
She literally ate nothing but yoghurt and breadsticks for a month and would rather starve than eat anything else. I'm serious. I was in despair. Mealtimes were so stressful and when she did start eating a wider range of food I would rather cook 2 or 3 meals for me, her and DH than argue about it.
Then DD2 came along when DD1 was 5 and DD2 needs a strict diet for medical reasons. I was too tired and busy to play silly buggers with food and within days decided that (within reason) I was only cooking one meal and if she didn't like it tough, that was it until the next meal.
This was a girl that would literally sit and pick any green specks out of cheesy pasta where I'd mixed broccoli in.
Over time of me being tough, consistent and really turning it around so that food/meals were No Big Deal she began eating more and more. I would cook dinner (if I was planning something that I knew she really didn't like such as chilli I would make her a separate portion of mince with sauce with no chilli powder or kidney beans but it would have all the other veg in it) and serve it.
We'd all sit down and eat and ignore her apart from the odd "oh well done for eating a bit of sweetcorn, it's yummy isn't it?" comment.
Plates would be cleared away with no comment, and if she hadn't eaten much I wouldn't say anything but she would still get pudding - they only get fruit or yoghurt anyway. I didn't want to make some foods "good" and a reward for eating the "bad" stuff eg veg. It's all just food.
She is now 12 and a delight to feed, and will eat literally anything. She loves it when we have fajitas - her sisters love them too. DD3 is 4.5 and loves to make her own wraps with tortillas, salad, cheese and meat.
Sorry this is so long but I just want you to know that I've been where you've been in a way and it does get better but you have to be strong, consistent and really take the focus off food so it's not such a big deal.
You must stop buying the pop and sweets as children really don't need them, especially young children. Keep them for very special occasions!