I'm trying to lose weight, and I just began cutting out diet sodas and any drink with sweetener in it because I heard that can cause an insulin spike and make you hungry all day. I usually start with a banana for breakfast. A handful of whole wheat crackers for a snaker. A small sandwhich and a salad for lunch. sometimes raisen bran for a snack or something of the like. Is that enough to do the job?

If you can add the following steps to your diet it will be perfect:
1) Eat more fibre
2) Drink around 1.5l of water per day
Good luck

Sounds like you're starving yourself. Think of veggies as "freebies" You can eat an unlimited amount because they are sooo healthy and have vitamins and whatnot.
ARE YOU TAKING VITAMINS? You should be.

What about dinner. You still need to eat a balanced meal in the evening as well. Unless you are extremely over weight you will gain back weight if you do not get at least 1200 calories (about) a day.