It could be that they were line dried, it could be detergent build-up, it could be hard-water mineral build-up, it could be age or it could be a combination of any of the above.
Try washing them once with very very very little detergent, if any at all (normally you'd only need 1/4 - 1/2 of the 'recomended' amount, use even less than that now). Dry them in the dryer and see what happens.
If they're still really rough you can try stripping them to remove the build-up. Stripping is just basically one or more really hot washes with no detergent... To help the process along you can try soaking them in the washer with a good amount of vinegar (the acidity will help break down the minerals or detergent). Say at least 3-4 cups at minimum, or even more if you'd like.