Why am i getting these strings of saliva in my mouth sporadically?

Saliva is good: Strings of saliva? Saliva in the mouth is a good thing... If it is "stringy" it may be that you are dehydrated. If you notice... Try increasing hydration. Acid reflux can also change the consistency of saliva in your throat and make it thick.

Cinnamon..: ..Flavored toothpaste can sometimes create this effect also. If you recently switched to this flavor of toothpaste or have started using cinnamon flavored candy or cough-drops, that may be the culprit..

Cheek lining: Without seeing you, can't definitely say. Often times what you seem to be describing is the soft tissue lining your cheeks sloughing off because of using a toothpaste with sodium laurel sulfate in it. Check the toothpaste label for this chemical. If present, use a toothpaste without it and see if the strings stop forming. The chemical is used as an engine degreaser.