I wouldn't try it w/o a serger.

Two sizes is a lot of altering and you may not be very happy with the finished results.

You might do better to take them to your local consignment shop and trade them for smaller sizes. Or sell them on Ebay to recoup a little of what you paid.

Congratulations on the weight loss.

I have watched a couple of craft tv shows that show remaking sweaters and jackets. Looks like fun, but they end up with a "funky" sweater. They cut off the sleeves and add socks for sleeves and stuff like that.

You might want to check out DIY on the net.

Please!!! do not try to do this job with a serger. If you are experienced in knitting, you will realize that every piece of yarn you cut, will be another piece that will come unravelled. This is not an easy job. Yarn in a ready made knit garment (other than double knits) should not be cut..so a serger would give you no assurance that you have the seams sealed to where they would not come undone. You will be very unhappy with the results.
From my experience in alterations, I would suggest that the seams be "relocate" but in that process, you are going ot have bulk to deal with as the seams will be several inches wide in all areas, especially the side seams. It is a job for only an experienced knitter who can do this task. I would not recommend a seamstress, but a knitter for this job. Save the sweaters and give them to someone if you cannot afford to have this job done properly. (I can give you more idea if you wish,)

If these are ready made sweaters that were manufactured by sewing together cut pieces of knit fabric, you might be able to alter them. A serger would be helpful, but I'd probably sew any seams with a regular machine first, then, after checking for fit, resew the same seam with a serger. Or, trim off the excess and finish the seams with seam binding or bias tape to enclose the cut edges.

But two sizes is a lot of altering, and I suspect that what you'll need to do to make them fit goes beyond just taking them in. You might need to alter the shoulder seams and the arm holes, also, at which point, we're talking about completely remaking the sweaters.

A quick test you can try is to stitch a stretched piece of elastic in the sweater along the shoulder seams, to sort of gather that seam. This will help the sweater hang off your shoulders properly, eliminating a pronounced drop shoulder from a too-large size. Depending on how bulky the sweaters are, this alone may improve the fit and allow you to wear these sweaters for a while longer.

CMC

My better judgement still says do not cut the yarn. I think many sweaters are made on knitting machines and they have a continuous length of yarn that goes from one row to the other. Agreed, there are some that are cut from knit fabric, but the general idea of sweaters is a Knit garment. There was a time when we had lots of knit fabrics to choose from. However, I don't see much of it today. The final word if CAUTION. I am not trying to override anyone elses opinion. This question offers us much that is unknown. Until then, I still think it is a risky project. Please inform us as to how this turns out. Each one of can learn something from her question.