"On the grounds of" - is what sounds correct to me. - I can't think of a sentence in which I would use the last three. It means that the statement or decision was 'built on the foundation' of certain things. Simply put, you can replace it with "for the following reason/reasons". I hope this is helpful.

Rachael, Thank you for your explanations.

Hi, as far as I know the first 3 are just variations of the same expression. It is basically another way of saying "because". The "ground" or "grounds" refers to the reason. For example, "He was fired on grounds of misconduct", which just means "he was fired because of misconduct." just in a more formal/official way. As for the last one, I had to look it up as I've never heard it said. Apparently it's a legal term. Thelawdictionary.org says this: "This term applies to the basis of the law suit and the facts that it involves". A variation of this I have heard is "legal grounds" eg. "legal grounds for divorce." In all these expressions "grounds" is like a metaphor, ground is another word for floor and is often used to mean "a basis". You could hear someone say, "on what grounds?" for example if they were arrested, meaning "on what basis can you arrest me?" I hope this made sense