I've heard: "I've to go the potty", "I have to meet Mr John", "Nature is calling me, I have to go", "I've to go to the rest room".
These sentences aren't formal, are they? Is there any other way that I can use it when I'm in a meeting?
I've heard: "I've to go the potty", "I have to meet Mr John", "Nature is calling me, I have to go", "I've to go to the rest room".
These sentences aren't formal, are they? Is there any other way that I can use it when I'm in a meeting?
In your examples I wouldn't put the first three in a 'formal' category. If you're in a meeting a must inform everyone why you are leaving "Excuse me, I just need to use the rest room" would be a perfectly acceptable way to do this. Depending on the meeting you could probably just say "Excuse me for a moment" without feeling the need to tell everyone what you're doing.
In the UK (I notice you've tagged this British English) "loo" is used fairly ubiquitously even in a semi-formal context. It is so widely used that it's become acceptable in all kinds of environments. It will obviously depend on your workplace but I would be able to use the phrase:
Excuse me, I'm just going to the loo.
at work and that would not be inappropriate. If you were in a more formal context you could say
Excuse me, I'm just going to the toilet.
You could substitute "bathroom" for "toilet" if you wanted to be more euphemistic, but if you wanted to be less explicit, I'd recommend avoiding the word altogether. "Bathroom" is not generally used in normal/informal conversation in the UK to mean toilet ("bathroom" normally means the room in your house which contains the bath, shower, toilet, etc.) but might work in a more formal context.
Excuse me for a moment
or
Excuse me, back in a minute
are less explicit.
To deal with one of the specific examples you gave, potty is not a word for toilets, it's a word for the pseudo-toilets small children use before they are used to using a real toilet (see pictures). Potty therefore is not a word you would ever use in a formal or informal context to refer to the normal act of going to the toilet. "Go to the potty" would be used, for example, when a mother was talking about her toddler. The key difference here is that a potty is actually a different thing to a toilet and you say "go to the toilet" when you're going to the toilet and "go to the potty" when you're going to use a potty.
"Use the bathroom" is the most common euphemism, at least in the UK.
Some other alternatives:
In a highly formal context the whole issue would be avoided. If you're about to close a big deal, hold it! And you don't see the Queen asking Mr President to "use the John". Instead she tells one of her aides, who tells one of his aides.
These sentences aren't formal, are they? Is there any other way that I can use it when I'm in a meeting?
They are not British, either. I mentioned that because you tagged your question as British English.
In the UK at least, the only context in which people talk about potties is when discussing little children who use an actual potty http://dictionary.cambridge.org/dictionary/british/potty_2 This has no meaning when discussing anyone else who uses an actual toilet.
Restroom is part of American English in particular http://dictionary.cambridge.org/dictionary/british/restroom?q=restroom , and is not used in the UK.
I don't know about your other, two examples but, they are not British.
If you want a way to say that you need to use a toilet, particularly a formal way, there is nothing wrong with saying I need to go to toilet or I have to go to toilet. You could also say I have to go to the lavatory but, that is rather old-fashioned and not as common.