Ah ! tht's ur problem.

U need caps across them too.

And u need a varistor across the primary of the transformer plus a 0.1uf 250V capacitor

Those will suppress the spike from getting into the transformer

 

Ah ! tht's ur problem.

U need caps across them too.

Caps, caps, everywhere!

So caps right across output of transformer? How big?

 

Something like this across the solenoids and the transformer will stop the spikes.

Choose the Varistor Voltage from here

 

Something like this across the solenoids and the transformer will stop the spikes.

So the spikes are coming through the transformer secondary and carrying through to the 7805? How come I don't see any spikes at the output of 7824?

Choose the Varistor Voltage from here

It just links to the search page.

 

I had it wrong.

Either way it's better to use 275V Varistor if the mains is 220VAC and 175VAC on a 110VAC line.

The spikes are back emf from the solenoids connected across the 24VAC tap.

There are two ways to stop it. Use a second transformer to power them
Other way is to Varistor across the secondary.

U have 24VAC at the secondary. so a 30V one will suite u, but I don't think u can get that low value.

I dunno if this method will work, but it's worth a try.
Find two 27V to 33V 1W zener diodes and connect them back to back across the secondary of the transformer

{ed}
I changed the zener value after thinking for a while.
15V will short circuit the 24VAC

 

I had it wrong.
U have 24VAC at the secondary. so a 30V one will suite u, but I don't think u can get that low value.

What power rating of MOV? I found 30VAC MOV's on digikey.

My inductive loads are 8Watts each. And 4-5 will be connected to the transformer secondary. (not all on at once)

 

Really ! 30V MOV's ?
Get 'em and connect one across the secondary.
As for power rating, does not matter much. Get one that satisfies u or is there any professor here who can calculate the back EMF generated by the OP's solenoids, so OP can find the energy value that he needs for the MOV.