connecting Wheatstone bridge to pin 3 of LM324 changes voltage?
Here is a 5 second answer to start.  First, put a decoupling cap (0.1uF or something like that) between LM324 pins 4 and 11 (its just good practice).  Just for testing connect LM324-1 to LM324-2 (unity gain), because an OpAmp is meant to be used with feedback.  

Of course you know that you will need a differential amp sensing both sides of the bridge to get any advantage out of using the bridge.  

Edit  

Thanks for adding the schematic.  

The output differential stage, as drawn is positive feedback.  So, you will need to exchange pins 9 and 10 of the LM324 connection to have negative feedback.  

Also, I didn't think about this much earlier, but the 4th channel would be best to be connected as a voltage follower with the (+) input connected to return.  I know that each channel is supposed to be independent, but they are not quite really.  The die will have parasitic structures that can affect all the channels.  For example, parasitic SCRs are common in many monolithic ICs.  So, it is always best to have all channels connected.