The BIOS may have an "Alarm Clock" setting that can power on the PC at a specified time. That should also bring it out of hibernation.
Turning it off again could be tricky. AVG 7.5 can be set to turn off when it finishes scanning, but that has to be manually checked after the scan starts.
Easiest way is to have a batch file check to see if the scans have completed by checking to see if the AntiVirus/Spyware/diskkeeper processes are still running. When the processes stop, then shutdown the PC.
You could also just have it shutdown at a specific time, but the scans may not be finished.
If the software creates a scheduled task job in the Scheduled Task folder (Control Panel | Scheduled tasks) there is a setting to Wake the Computer to run the task. Right click the task, goto the Settings tab and check the box.
Otherwise, you'd have to check each program to see if it has an option to wake the PC, or bring it out of standby.
HTH
Jerry