Well, it's legal to splice these connections in a J-Box, though I just don't like the idea of it being outside. It would have to be in a weather proof box with gaskets. I would also use 2 box's instead of one since running more than 3 cables together may affect the voltage. These cables would need to be sleaved for protection where they come through the house and you'd need to do a box fill calculation on the j-box's to make sure that they are sized properly. Here's a link for you for this:
http://www.taunton.com/finehomebuild...ges/h00134.asp
Your other choice may be to install these Jbox's inside the home, but then they would require to remain accesible at all times.
Another possiblilty would be to install a sub panel on the outside of the kitchen wall to power these circuits.