When will SKT and Championship skins go back on-sale?

SKT skins? Probably when the Samsung White skins get released.

Championship skins? Riot does not currently have plans to re-release those. Same with Victorious and Challenger skins.

Edit: Evidently I'm badly misinformed.

They usually come back during the big events. All-stars, which usually in May is the time when we see the Team Skins and then Worlds around October is when we'll see the Championship (with the exception of Championship Riven, as that was limited and won't be seen again before at least 2016)

Oh, I currently have 4k rp and saving it for upcoming champions and those skins so I hope I'll not get tempted to used all the RP before those skins are release because I have the hobby of spending it all really fast.

Well, to be honest, I want Championship

Here is the info about legacy and limited skins. About when they may come back, i think during championships this year. https://support.riotgames.com/hc/en-us/articles/201752944-Guide-to-Legacy-and-Limited-Skins

Actually full announcement for the Team Skins is right here http://na.lolesports.com/articles/more-mid-season-invitational-tickets-coming-soon and they will be returning very soon as this begins on may 7th.

CS Shyvana during the World Championship which takes place in about October-November.

SKT T1 Zed ... SoonTM

Oh, may 7th, that'll be nice :)