"If I disconnect the water valve, then every thing is fine, meaning there is no oscillation. What could be the best way to approach this issue? "

Forget the best way. There is only ONE way. Just beef up your power supply. The poor fellow seems to be struggling to supply what you want. The long period of oscillation ( 0.3 sec or so ) is very characteristic of poor power supply regulation - as I told it is a chatter.

And I think we have a reached a stage where one needs to know certain things :

1. What is the rating of your power supply ? Volt and Ampere ?

2. What is the rating of the water valve solenoid ? VA rating or Watt rating as per data sheet.

3. And telling us about your exact power line routing will help locate the problem. Like where you tap off power for the relay and solenoid etc. And most important your grounding scheme will also need to be known.

( Dont worry - once you tell me the above I will not tell it to anybody. Secrecy assured ;-) )

Raghu