First, make sure all paths objects are in the paths panel in photoshop ( window -> paths)
then go to File-> export -> path to illustrator..
this will save all paths in an illustrator document.
open the file in illustrator, the paths will be invisible ( unpainted objects) you can press ctrl + A to select All,
or you can press ctrl + Y ( to see them in The outline mode) you can now select each path with the selection tool give it a fill color ( make sure to press ctrl + Y to get out from the outline mode )
there is one more Tip,
In photoshop, click on one of the paths in the paths panel, press ctrl + c ( copy) and paste in illustrator ( ctrl + V )