Classic Relays
Set up a classic relay race in which your guests divide into teams. For a more ancient Greek feel, perhaps the relay object is something like a conch shell or an olive branch. Set up a track. Most likely, you won't have the space for an oval track, but a straight line can do. Either have the teams split up their members at each end of the track, requiring the runner only run the length one direction, or have runners reach the end and come back to pass the relay object on to the next team member.
Add Obstacles
To make the relay race a little more challenging, add in a few obstacles like hurdling or obstacle course training. You can set up low benches to jump over, lay out tires for jogging through, or even have a rope swing hanging from a tree that requires participants to swing over a mud puddle or wading pool of water. All the while, the runners must still keep hold of the baton.
Add Challenges
Make the relay even more challenging with your choice of relay object. Instead of a simple baton (or the shell or branch), have the relay teams carry a bowl of water. Spilling the water costs the team a lap as they must refill the bowl and start that lap over. Or use something more fragile, such as an egg, that participants must carry on a spoon and pass from back and forth. Breaking the egg can cost the team the game or the lap.