they all mean almost the same thing, they are all pointing out that something is unique about someone, or a situation. However, there are tiers of uniqueness, and some are viewed as positive or negative.
weird, strange are associated as negative words.
He looks weird. (something about him makes him stand out in a bad way)
That is a strange outfit. (the outfit does not make sense, doesn't match)
Bizarre I use this word to explain situations...not usually a person.
That was a bizarre storm. (the storm did not follow the pattern of a normal storm)
peculiar, odd these two are not negative but simply pointing out something/someone was a bit different.
She is a peculiar cat (the cat acts differently from other cats)
The way she walks is a bit odd. ( she walks differently from others)
unique is another word that can be grouped with these words and this word is a positive word.
Her sense of style is unique. (her style is different from others, but in a good way)
So from weakest word to strongest word
odd, strange, peculiar, weird, unique, bizarre
I hope this helps!!