You can turn on or off any of the Skype notifications for your Android phone from the Notifications menu.
To access Notifications
Turn off all notifications: Tap the Notifications slider at the top of the screen to change it to OFF.
Turn off new Instant Message notifications (for 1:1 chats): Tap the New instant message slider to change it to OFF.
Turn on Group Messages: Group message sync is turned off by default to save battery power. To turn this feature on, tap the Sync group messages slider to change it to ON.
To turn on or off notification sounds, lights, or vibrations, use the checkboxes next to those options.