Very small 1cm swollen lymph nodes under arms. Been there for a year or so. Very soft and moveable. No infection. Why is this?

Could be normal. Several lymph nodes are present in your axilla. In thin patients these lymph nodes can be easily felt. The presence of a lymph node is not an abnormality. Should it change in size, become firm and immobile, or if you have other worries about it, see your friendly doctor.
Fatty tumor. Likely it is a lipoma which is a benign fatty tumor. If it bothers you or if it grows or changes characteristic then have it removed.