for a jogless join one of the easiest methods is to cast on one extra stitch. At the start of your first round slip this stitch and then knit around to the last stitch. Then knit the last stitch together with the slipped stitch.
It is possible to carry the colour you are not using for the stripe up the inside of the sweater. At the start of every round, twist it around the colour you are knitting with. When you need to change colours, just drop the colour you have been using and pick up the new colour giving them a twist. This cuts ou the need to cut the yarn on every stripe and weave in dozens of ends.