Sound travels very well through water - try isolating the tank sonically or mechanically from whatever you can. This could be as simple as putting a dampening material (carpet!) under the tank. It is a long shot, but I think it warrants an answer rather than a comment nonetheless.
I once wasted a day trying to fault-find a sensitive differential amplifier circuit that was exhibiting almost exactly what your tests are showing: a ~1-2kHz single sinusoidal pulse every 20ms (or the 60Hz equivalent in your case), but no actual mains frequency sinusoid. We tried turning the lights off in the lab, the computers, equipment in neighbouring rooms, everything. We tried laptops, all manner of electrical shielding - we put a grounded tinfoil 'hat' over the circuit board - and even resorted to working by candlelight once it got dark.
When we knew we had lost the battle my tutor rested his head on the desk in defeat, with his ear to the surface, and heard the spurious signal; the desk was vibrating. We determined that the building's cooling/heating system was the source of the excitement (pun intended); it was roughly beneath the lab and the noise could be heard faintly in the corridor outside its room. A heart-warming story.
In the end someone put a scarf underneath the circuit and the interference was gone instantly. Even with the nearby electrical equipment turned back on, mechanical isolation prevented any unwanted signals.
I'm not sure specifically about the noise on your circuit, but here is a pretty extensive help guide for laying out TIA circuits:
http://www.linear.com/solutions/5633
I can't tell if you have voided the ground and power plane on your input trace from the photodiode. However, you might try the following. Stand the input cap and resistor on end (tombstone). Solder a very fine wire (40AWG perhaps) from one end that is airborne to the photodiode output pin. This will minimize the input capacitance, and thus give you the best high frequency response.
Another less drastic thing to try is to trim the pads of Rf and Cf to the smallest possible, then solder them on the board sideways. Parasitic input capacitance is your enemy at high frequencies, and both these ideas are aimed at minimizing it. Although expensive in mass production, it may give you some ideas to make it better performance.
Some other ideas - use 0402's instead of 0805's or 0603's. This will decrease input capacitance as well.
Another idea that was also in the LT literature was to run a ground trace between the pads of your input resistor. This brings the field strength to 0. I honestly don't have a good feel for how this helps, but they wrap some words around it in the link I gave above.
Good luck! You should post some screenshots of your frequency response and let us know what you did - what worked and what didn't.
Best Answer
Too long for comment: To expand on @passerby a bit - the noise you hear is the result of the water forming a partial short-circuit between the two wires that come to your house from the telephone exchange; because of various chemical effects due to electrolysis, gassing, etc this is a lot more noisy than bridging the line with the equivalent resistor. Often the characteristics of this partial short are such that it will 'ring on' - ie application of the higher-voltage AC ringing will cause the resistance to drop; this appears to the exchange equipment as if you have answered the phone, and it will stop the ringing current and open the transmission circuit; this kind of fault is called 'Ring Trip' in (British) telephone engineering jargon.