Inexpensive keyboards are usually made with an elastomeric ("rubber") membrane that sits over a large printed circuit board. When you press a button, the plastic key collapses the dome, whose bottom has a conductive pad that can short contacts on the PCB.
If keys are not responding, it may simply be due to fouling of the pad/contact, so disassembling and cleaning should fix the problem. Clean up as much bulk residue as you can on the PCB with water, then do a final clean with alcohol. The elastomeric membrane you should be able to immerse to clean, but a final clean with alcohol may be prudent on the bottoms of the domes.
Keys being confused with one-another may indicate some additional damage to the logic, parts may be damaged irreparably, or the juice residue may simply be shorting some high impedance pins, causing confusion. A good first step would be to clean it in any case.