Check out my Word 2003 help's link:
http://office.microsoft.com/assistance/hfws.aspx?AssetID=HP051866641033&CTT=1&Origin=EC010227221033&QueryID=2vY7Htujn&respos=1Ctrl-S in Word has been Save for decades and is common to many applications, from Word and Excel to Notepad. That was the point of my posting: all those keystrokes have been around for that long in many applications.
What version of Word do you have? Are you sure you're not operating in WordPerfect mode and your keystrokes aren't reassigned? I can't find anywhere in the help that there's any keystroke for Insert Symbol.