Both 完了 and 終了 seem to have the connotation of finished/complete, but what is the difference, if any, in usage?
完了 kanryō means "completed", while 終了 shūryō means "ended".
式典の準備は完了した - The preparations for the ceremony are complete.
祭りは夜更けになってようやく終了した - The festivities finally came to an end late at night.
The video game Star Fox 64 uses 作戦完了 when you fulfill your mission objective, and 作戦終了 when the mission is over but there's some objective you haven't fulfilled. The English version translates these as "Mission Accomplished" and "Mission Complete", respectively. So perhaps 完了 suggests some kind of fulfillment, and 終了 is more neutral.
I think 完成【かんせい】 has the meaning "completed" with the nuance "Well done!" But, I'm not positive.