I'm a Linux user and for wireless transfer (sometimes I use USB), I use sftp.
If I want to access the PC's files from the Android, I use ES File Explorer. The PC needs to be running sshd.
An alternative wireless method to this would be to run samba on the Linux PC. Again, files would be accessible via something like ES File Explorer. They would also be available to Windows PCs on the network.
If I want to access Android files from the PC, I can run a ssh server (currently ssh Droid) on the Android. I use the Dolphin file browser on the PC.