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It seems you have ground loops, and possibly having multiple ground connections shorting out your signals.  Your hand-sketched diagram is a good start, but you need to show <b>all</b> the ground connections.

The scope is presumably grounded via its ground lug that plugs into the electrical outlet.  Let's call that the "power ground".  You show that with the chassis ground symbol in your diagram.  But then what's the ground connected to the reference electrode really connected to?  Using a different symbol means it's not the same as the power ground, but what is it?

You mentioned that the opamp is powered from a power supply derived from a computer's USB.  That is also most likely referenced to power ground.  Show that in your diagram.

I'm not familiar with the details of pH meters, so don't know what the significance of the reference electrode is.  You don't seem to be using the output of the reference electrode, so it appears it's job is to float the solution at some voltage.  However, you also show an explicit connection between the solution and power ground.  Something is wrong here.

I would start by eliminating ground loops.  Make sure your whole setup is referenced to ground <i>by exactly one path</i>.  That should probably be your scope ground lead, since that's the hardest to avoid not being connected to ground.

Use batteries to power the opamp.  Not only do they inherently float, but they will also be much less noisy than something derived from USB power.

I can't say what to do about the reference electrode since I don't understand what its function is supposed to be.