Can a Power affect one creature three times if it has the ability to affect three targets?

No it can not. You can only affect a target with a Power one time during a turn.

Example

A player character uses a power that can affect 4 targets within 4 spaces. There are only two targets within 4 spaces of the player character. Only these two targets can be affected. Each target will only be affected by the Power effects one time. They can not be affected twice due to the Power having more targets than can be hit at the time.