I'm no ABS expert either
I'm just stabbing in the dark regarding your problem.
The solenoids are electrical magnets that operate valves in the valve block. The valve block is the alloy part that the brake pipes connect to.
When the ABS kicks in the solenoids operate the valves which work to stop the wheels locking up.
I'm thinking that maybe your valves could be sticking or something, maybe this could be because of the brake fluid, so it's got to be worth changing it to see if it makes any difference as it's the cheapest option to start with.
If the problem is no different after changing the fluid well then you will have to look at changing the ABS unit, I would probably try a 2nd hand unit from the breakers.
Changing the brake fluid....
I would recommend using a pressure bleeder to change the fluid, but failing that the old pumping the pedal method will suffice. Just make sure not to push the pedal right to the floor when bleeding, try to only push it as far as it goes under normal everyday use, half way down as a maximum.