Hi,
Firstly, No flavoured water should not do any harm, but I wouldn't do it again! The water does not get 'used' and circulates around the engine and radiator, so the added strawberry flavour should have no detrimental effects unless it reacts with the coolant (which I doubt).
However, like other posts have said, the coolant level will not just suddenly drop for no reason. Either there is a leak somewhere (radiator, water pump, hoses), or the head gasket is allowing water to escape.
Seeing as the car overheated, I would suggest that the coolant system be checked over to ensure that there are no leaks or blockages, the thermostat and fan are working, and there are no problems with the head gasket.
A quick check of this is to see if there is a white mayonnaise-like substance underneath the oil cap, or if there is any oily residue in the water.
I would suggest that you don't drive the car very far until these are investigated.
Should any of these parts need changing then the coolant should be drained and replaced anyway, solving your problem with the strawberry water!
Hope this helps,
Lee