Electrical – Solid State Relay Stuck in Closed Position

You didn't link to the relay module in question (I see you're new so no worries, please try to do it next time ;-)) but I'm assuming it's this one.

If this is the case, then I think you have mistakenly connected the 26.6 VAC supply to what is meant for a 5 VDC supply. If you have this is not good, hopefully it hasn't blown anything (very possible though)

The marking are actually VCC (not VOC) and GND. TO these you need to connect a 5VDC supply as mentioned.

Here is a schematic of one of the relays on your module:

Notice the 5V on the input side of the relay. The "switch" is from pins 3 and 4 with a fuse in series.

For the relay connections, they act like a single pole single throw switch (SPST) and need to be in series with the power source. To switch the power to the solenoids, you need one lead from the power supply (either one as it's AC) to one of the relay terminals, then one of the solenoid leads to the other terminal. Finally the other lead from the solenoid connects to the other supply lead.
Just try to think of the relay as a simple switch.

It varies depending on the SSR.

Really, every photo-coupled device will need some sort of current-limiting device, the question is just whether there is a resistor or some similar part built-into the SSR, or whether it needs an external resistor.

In this situation, the LCA710 is probably less accurately described as a SSR, and better described as a photo-activated MOSFET. You will need to provide your own current limiting.

In the datasheet, you can see they explicitly specify a maximum Input Control Current, as well as the Input Voltage Drop. If this were a traditional SSR, they would just provide minimum and maximum voltages.

What the datasheet means when it says TTL/CMOS Compatible is simply that the current required to turn the FET on fully is within the sourcing capabilities of most common TTL/CMOS devices. Some optos can require upwards of 20-30 mA to turn on fully, which would prohibit them from being used with most common logic devices without an additional high-current buffer.

It's also worth noting that this is pretty much spelled out explicitly: the datasheet says Low Drive Power Requirements (TTL/CMOS Compatible). The critical part here is the "low drive power" bit.