They have weird party names. I'd like to know the history behind them.
Both PO and PiS are very recent. Both were founded in 2001. LiD was formed as a coalition in 2006, and the four parties in LiD were founded in 1999, 2004, 1992, and 2005 respectively. LiD doesn't exist anymore either, they all went different ways.
PSL, "Polish People's Party", in English, is in yellow-green. They are socialists who have reformed and might now be closer to Christian democrats in the traditional European model;
PSL are agrarians.