i expect my suggestion will horrify a few folks, but if it was me (and .... er ... ummmmm .... it has been me more than once in the past :lol: ) i would cut new strips and start again. toss the wonky strip set into the scrap bag.
you will spend more time trying to make the ones you have work than you would spend just starting over. if you don't have enough fabric left to do that, i'd either:
1. buy more fabric. if they don't have enough of the ones i was using, and i couldn't substitute, i'd buy whatever i needed to start over with different fabrics and make something else from the first set. only if the cost of the new fabrics is an issue (for example when i have to meet a deadline and won't have the money i need in time) i'd choose one of the next two options.
2. take the strips apart, starch press each one flat, and use my ruler to see if either edge is straight. if there's at least one straight edge on each strip they can be used the way you described - although i wouldn't worry at all whether everthing matched exactly at the ends. just make sure you don't try to sew two wonky edges together. for each seam, make sure to pin the strips together so that you have at least one straight edge to use as a reference for your quarter inch seam.
or
3. take the strip sets apart and straighten the cuts. that means working with narrower strips, so you'll have to remember to make all future strips the new width and your quilt will be a little smaller.
again, i wouldn't worry much about whether or not the sewn strips match exactly at both ends of the seam. you're going to cut it up anyway, and the pattern shouldn't include using the selvage edges so the mismatched danglies shouldn't matter.
life is too short and quilting is supposed to be fun. no matter how small or simple the project, i make at least one goofball mistake during each and every one. i have learned to look at them as unplanned lessons. way cheaper than a class in a shop - even when i factor in the cost of the fabric. :lol: i've also learned to always buy at least a half yard more than the instructions call for. i nearly always need at least some of it. :oops: