From strongest to weakest, they are:
Weird - strange in a negative way, in a way that makes you feel uneasy.
Strange - can mean weird, but more noticeable, making you look again. It is not as negative as weird, but still negative to a degree.
Odd - a weaker form of strange and weird - something that is not normal and is noticeable, but not in as strong or shocking a way as the first two.
Awkward - odd, but also embarrassing. It is usually used in a situation where something odd and embarrassing has happened and nobody wants to be the first one to say so.