Кусок it's a big piece, кусочек it's a small piece, часть it's pretty big part, частица or частичка or маленькая часть it's a small part. And the difference is in cases when we use it. Кусок for example is about pie, часть we would use when we would talk about soul. Yes you use any of it but quiet unusual to tell, кусок моей души, and дай мне часть пирога. Better частица моей души and кусочек пирога