The chief active ingredient is tea tree oil, aka Melaleuca, which has many many claimed health benefits. It also contains bromochlorophene, which has been proven to reduce plaque and gingivitis. Another ingredient is Agrimonia euphoria, which has been stated to have medical and magical properties since the time of Pliny the elder (23 AD).
Stoma, in Koine Greek means "mouth." In English it can refer to something related to colostomies - I didn't want to give much research in that direction!
Odol decided to color the paste a light green, with just a hint of blue. The flavor is medicinal and slightly in the realm of mentholatum.
My sister Amy bought it for me. (Thanks!) Sadly, unless you live near the Czech Republic, I don't think you can get your hands on any.