Hows is it acting strangely?
Virus and trojan, yes go ahead - scan away.
It is possible to look to see if someone has been on your computer...
1) Fingerprint the keyboard
2)Contol panel > Administritive Tools > Event Viewer > have a look at the logs - Good look though, if you can remember the time you logged on to your cpmputer then your ok if not then forget it.
Also install a firewall.