When do you want to go?
 
Does it matter where in Greece?

Probably www.canadian-affair…. to the UK, then www.easyjet.com or another low-cost airline to Greece; more at www.whichbudget.com (I would add Globespan, but their service from Calgary doesn’t re-start until May).

Checking prices with ITA, Zoom, Air Transat, etc… looks like British Airways has nonstop flights Calgary-Heathrow in April for $634 rt total, and with excellent flight times—8h, 25m going and 8h, 55m return.

From Heathrow, Alitalia has Athens at $271 rt total with flight times that should give you plenty of time (3.5 hours minimum) to make connection on the other ticket.

Total = $905.

Otherwise, I see NW/KLM with 2 connections (MSP and AMS) at $1042, and Lufthansa with 1 connection (FRA) at $1057.

Since you didn’t give exact dates, I used ITA and searched the entire month of April usind 6-8 night stay. These prices are cheapest I saw.

Maybe saving the best for last…. Using http://flights.eurot… found $931 CAD with Air Canada. The total travel time is a little long with this, but if you miss a connection, you’re covered to get on the next available flight—unlike using the BA+Alitalia method I described above.