Distortion may be caused by a dirty volume control. It may also be caused by leaky condensers. Check all condensers for leaks, and replace all which have any leakage what-so-ever. Check resistors for drifting, too. Remember to remove each component that you test. Leaving components in the circuitry will throw off readings.
Also check tubes. Occasionally a tube will get gassy or weak, and will perform as you stated (distorts easily).
Thomas