The Kimono Girls are girls that will appear regularly during the course of HGSS Johto story line.
Just to let you know, there are spoilers in the below paragraphs if you haven't played this game before.
The Kimono Girls are women that dress like Japanese geisha women. They are very traditional that come from the oldest, traditional place in the game, Ecruteak City.
Ecruteak City is home to two towers. The Burnt Tower, the place where the story of Entei, Suicune and Raikou took place - and The Bell Tower (I think, I'm not sure. Sorry >.<) where Ho-oh is. The Kimono Girls start from a long time ago, and are very old. (Not the girls themselves, the Kimono Girl title - geisha, to be exact) Therefore, they know a lot about these traditions. They were able to re-enact the dance to bring Ho-oh and/or Lugia.
The reason they sounded freaky when they gave you the Togepi egg was because they had faith in you and they thought you would become an incredibly good trainer. They put this to the test later on as you battle all of their strong Eeveelution Pokemon consecutively, which you would successfully do and awaken the legendary Pokemon Ho-oh and Lugia. They aren't psychic - I don't really know what they are. xD
There aren't any spoilers here
Let's just say, they know a lot about the back stories of the legendary Pokemon in the game. Their dances and their other thingies come back from a long time ago, therefore they are very traditional people. You will learn a lot more as you progress through the game.
Hope I helped. :)
Source: Experience