What causes delayed onset muscle soreness after resistance training and are there any non-drug ways to alleviate it?

DOMS is complex: The answer to this question is complex, especially in the "what causes" portion. Although you may find some symptom relief with rice/ massage, "it is important to be aware that pain reduction does not represent recovery". You will need adequate recovery time even once pain/ soreness subsides. The acsm has great info at http://www.Acsm.Org/docs/brochures/delayed-onset-muscle-soreness-(doms).Pdf.