This all depends on where you come from. Here goes:
1. Bathroom: This is a room in your house, or in a hotel, where you wash. Bathrooms usually have a bath, a shower, a toilet and a washbasin. In British English, this is the only meaning of the word 'bathroom'. In American English, though, 'bathroom' is also used to refer to any room containing a toilet. For example, if an American person needs to 'answer a call of nature', they will say 'Excuse me, where's the bathroom?', even though they really mean 'toilet'. It's considered vulgar in American English to refer to toilets directly.
Toilet: This is the porcelain object which you sit on to ... well, no need to explain. In British English, it's OK to say 'Where's the toilet?', meaning 'Where is the room containing a toilet?'. This isn't acceptable in American English.
Restroom: This is the equivalent of 'Where's the bathroom?', used by American English speakers, particularly in more public places, such as airports or shopping malls. It doesn't mean anything in British English, other than (perhaps) a room where you might rest. I can't imagine where this would be, though.
Washroom: A room where you wash. It's not a common term. A hospital or dormitory building might have a washroom.
Lavatory: A rather old-fashioned term for a toilet. It is rarely used nowadays.