I would expect that to mean that it is a regular occurrence--that the speaker stays at his uncle's place every summer.1-I stay at my uncle's place in the summer.
Those mean pretty much the same thing. The speaker expects to be staying at his uncle's place during the upcoming summer.2-I am staying at my uncle's place in the summer.
3-I am staying at my uncle's place this summer.
I would expect that to mean that not only is he staying at his uncle's place but he expects to be there for the entire season.4-I am staying at my uncle's place for the summer.
[Edited for spelling]

Academic