"Once-over" is usually applied to an examination of some sort. Examples: "I gave my question a once-over for errors before I posted it." Or, "My son cleaned his room but I gave it a once-over and he didn't do a very good job."
"Twice over," "three times over," etc. generally only refers to the repetition of events. Example: "The car was so dirty that I had to wash it three-times-over." The "over" also usually implies that under normal circumstances, repeating the event that many times would have been excessive.
"Twice," "three-times," etc. without the "over" can refer to events but can also refer to multiplication of nouns. An event example can be as simple as, "I washed the car twice a month." A multiplication of nouns example would be, "I had two oranges and then somebody gave me four and now I have three times as many."