iam from germany and need help. Can anybody correct my first sentence from my story my english is not good?

It's

"It is a rainy and stormy day and Jayson's family have bought a small, cozy, uninhabited house in a little town, which they're moving into today."

Unfortunately this doesn't translate directly so I've had to restructure it a bit. Good luck!

Jayson's family bought a small, cozy, uninhabited house in a little town, moving into it on a stormy, rainy day.

jason's family bought a small, cozy, uninhabited (vacant?) house in a little town. Today is a rainy, stormy day and they are moving in.

that might work, depending on exactly what you are trying to say.

The point of the way i wrote it is that it is a nasty weather day and they are moving in during that nasty weather, which is the only reason I can imagine that it matters what the weather is (why you even mention the weather)

Erm, you could mean...

Jayson's family have bought a small, cosy, uninhabited house in a little town. They are moving in today, when it is rainy and stormy.

Its quite hard to tell because you have got different amounts of people and tenses and stuff. Good luck though! :D