In Oregon, it it legal to leave religious tracts in public places? Would it be considered littering?
It is legal, and it is illegal given the First Amendment to prohibit distribution of viewpoint literature in a "public place", if you mean "on government property". There are a few exceptions such as "on a military base" where expression is encumbered, so you would have to be more specific about where this takes place – any such restrictions would have to be general and could not specifically target religion. It is not "offensive littering" which is a state crime. Non-offensive littering is governed by municipal ordinances such as Eugune's, that
No person shall throw or deposit or cause to be thrown or deposited any glass, metal, broken ware, dirt, timber, brush, rubbish, garbage, filth, or litter on public or private property except in such places as may be designated by the council
but distributing literature does not fit that description (it isn't "throwing" or "depositing" the enumerated substances on property, it is "distributing"). The city might tell you to pick up the flyers if you put them in a pile outside and they get blown all over the place, but it's not clear that they can, under Oregon law, legally force you to gather them up.