Things to do:
1) measure coil resistance of the relays.
2) build/buy a 24V DC supply [full wave bridge rectify the 24VAC that runs the relays now, and 24V regulator circuit], or [buy a 24V DC power supply] that has enough current ouput to drive at least 8 relays [a little extra for Murphy], and also 3.3V or 5V regulated from the 24V for the micro. Tie the negative of both supplies together [if it is not already. - you can find cheap supplies at http://www.mpja.com
, among other places. [a switching supply will waste less power than a linear supply] Replace the 24VAC [from a transformer] that you are now using with this 24V DC supply.
3) the ULN2003A has 7 inputs, 7 outputs to drive the relays [you will need 2 of the ULN2003A's], a ground connection and a positive connection that you will tie to the +24V positive [this pin is for the 7 clamp diodes that the ULN2003A has. each relay you wish to control connects from the 24V suppy positive to an output of a ULN2003A. If the relays are a long distance from your new controller's location, put a diode directly across each relay's coil, with the cathode of the diode to the side of the coil that connects to the +24V, and the anode to the lead that goes to the ULN2003A's. the inputs of the ULN2003A connect to the micro, to pins that have been programmed as outputs. driving one of the micro's output pins high will cause the relay associated with that pin [via a ULN2003A input/output pair] to be energised. To test this circuit w/o a micro, connect a ULN2003A input pin to the 3V or 5V supply.