I've seen and know some types of Kryptonite and know what its effects are, but is there something canon (or even non-canon) that shows what effects can happen when various different types of Kryptonite influence Superman at the same time?
Yes, there are several times when Superman is exposed to multiple kinds of Kryptonite:
Red and Green Kryptonite dust seems to rob him of his powers permanently (Superman #152)
A ray comprising Red and Green Kryptonite causes him to develop a third eye in Action Comics #275
Red and Gold Kryptonite gives Superman 'super-amnesia' in Superman #178
There are also two "imaginary stories" involving mixed kryptonite sources.
In Superman #192, Superman is subjected to an alloy of Gold, Red and Green Kryptonite. The effects are that he has amnesia and loses his powers.
In Superman #162, Superman exposes himself to the rays of Red, Gold, Green and Blue Kyrptonite. The effect is to literally split himself into two identical (and hyper intelligent) Supermen.