There are a lot of great suggestions here. I can only add that I've been where you are and it is totally frustrating! Relax! I finally gave myself permission to just do the best I can today and try for better tomorrow. Everything I ever made has mistakes, and I always finish a project knowing that if I make it again, I could do it better because I have found little things while working on it that would help next time. My quilting motto is "Better finished than perfect." I was almost paralyzed by the need for perfection. Each project is a little better than the last and that is all I ask for.

Have you tried the June Taylor shape cutter? It has slits at different intervals to put your rotary cutter in to cut.

I found that the table I was cutting on was sagging in the middle, which made all my cuts just a little off. The plastic table ended up with 3/4" piece of plywood over it to solve that problem. I have also found that if there is more then one fold, my cut pieces can have those lovely dog legs. I always wash my fabrics before I use them (I don't like the chemicals that are used in the warehouses on them), hang the fabric on the clothesline to dry and spray the fabric liberally with starch while the fabric is still wet. I always press the fabric before I cut it. Feline Fanatic is quite right in her answer. Hope you figure out what has caused this reversal of skills!!

If you use an Accuquilt you will get perfect strips. If you then press them and they turn out wavy, you are pressing wrong.

Are you squaring up your fabric before laying it out to cut? I watched a YouTube video on this and it made a tremendous difference. Here is an example of one way to square up your fabric.
https://www.youtube.com/watch?v=pSLwhogZk2A

The even surface tip is so important! I'm glad you brought it up. This was a problem for me for quite a while - until it dawned on me that my cutting surface was not flat. I fixed that problem and my cutting has improved.

The other thing I do that improved my cutting of strips - Assuming that you cut across the width of fabric, folded once selvage to selvage, press a sharp crease into the fold. That seems to minimize the curving at the center when I cut.

Lastly, I have learned the hard way that cutting through more than 2 layers of fabric - more than one single selvage to selvage fold - creates uneven cuts and curving. Maybe others can do more than 2 layers at once, but it just doesn't work for me.

The other thing that greatly improved my cutting was to spray baste the bottom of the ruler I use for cutting. The ruler clings to the fabric, so the ruler doesn't slip out of place while I am cutting. Note that I had to rub some of the spray baste off of the back of the ruler immediately after spraying. In some places it was too thick on the ruler. If you don't like the spray basting on your ruler, it can be washed off, but it takes a bit of elbow grease, soap and water or a vinegar/water solution.

The 1/4" foot with no guides works best for me, as well. I have one with a guide, but the guide hid the edge of the fabric so I couldn't tell whether I was sewing a straight 1/4" line.

My sister, on the other hand, loves her 1/4" foot with a guide. We all have to find what works best for us as individuals.

I was wondering the same thing about pressing vs ironing. Have you heard of and tried a steady betty?

Also, this video might help you get an idea of what's happening with your cutting. It could be you are not squaring up before cutting your strips. https://www.youtube.com/watch?v=yI8kkFnpwpM