Can you run HSRP with four L3 switches
(1 active and 3 standbys)? How can I load balance between them? I'm assuming that that a routed connection would be required between the L3 switches correct?
For HSRP/GLBP to work the switches need L2 adjacency. You can connect up your switches with L3 if you want but then if the switches only interconnect via L3 then HSRP/GLBP will not work.