I wanted to also mention that curving can be caused by holding the strips too taut, especially if the strips are not cut perfectly straight-of-grain. Holding the strips too taut while feeding them to the needle can stretch the edge that is being sewn. The more off-grain the strips are cut, the more easily the edges stretch. Bias-cut strips would stretch the most; that is why they require very careful handling.
I just noticed you mentioned in your original post that the strips were curving towards the right. To me, this indicates feed dog misalignment. If you were holding the strips too taut or if the presser foot pressure were too tight, the strips would curve to the left (because the sewn edge would be longer than the rest of the strip). Other possible causes, as mentioned by others, are that the tension on your threads is incorrect so that the stitches are gathering the fabric slightly and/or that the stitches are too close together. Normal factory stitch length is usually fine for piecing, though, so I would be inclined to blame tension first. It can be that both top and bobbin tension are too tight.