Is there any use if a file has only write and execute permission and not read permission?
There are uses for most objects you will find in a filesystem:
Named Pipes: The execute bit has no meaning for a pipe so this is the same as
Device Nodes (as usually found under /dev): Similar to named pipes - you could write to the device but not read from it.
Permissions like this can be used for drop box like functions on a folder, though you typically wouldn't use the write permission in that case. Other than that I haven't seen a lot of use for only write and execute. Thinking...