Is it possible to drive led strips using a halogen driver?
Your power supply doesn't like the LEDs.  That's not a surprise. Either 


because there isn't enough current flowing (the halogen acted as a dummy resistor to create some load), in which case more load will cure the problem.  Or 
the power supply needs to be able to leak current in both directions (AC) through the light. Halogens can do that, LEDs cannot.  Try reversing the polarity on some of your LED strips.  If they still light and it solves the problem, that's actually bad news - it means this power supply is outputting AC and it's not fit for LED strips. (not least it will make them shimmer at 60Hz, which will be very noticeable and much worse than 120Hz shimmer from obsolete fluorescents).  It's time to replace this power supply with a DC supply, that will both work with LEDs with no shimmer whatsoever, and also support halogens.