"throw out/away" vs. "toss (out)" vs. "pitch (out/away)" for "dispose of; discard; get rid of as worthless or useless" in AmEng
Solution 1:
Speaking for myself, the terms have basically the same meaning. However "Toss out" is a bit wordy for casual conversation. You can simply say "toss". In that context others should understand you intend to dispose of the item. The word "pitch" tends to put an emphasis on the emotional component of the act of disposing of the item.
Toss is used when you simply wish to be rid of the item. Pitch tends to show more determination. As if you want to damage the item in the process of getting rid of it.
Solution 2:
I've never heard someone say 'pitch' in reference to putting something in the garbage. Most common would be "throw" "toss" or "chuck," eg "I chucked it out" or "Throw it in the trash." Tossing has the implication of a lighter touch, like an underhanded throw.