As in an odd person out, yes. It equates to the English "Third wheel" (Or fifth wheel if that happens to work in your dialect)
That also works in French, where you'd be "la cinquième roue du carrosse" (the fifth wheel of the carriage). At least you get to be part of a luxury vehicle from fairy tales. :)
In Lithuanian we say something that would translate to "The fifth leg of a dog" :)
Never heard of that expression before and I'm from Lithuania as well. Great to learn new things! :)
In Italian: "l'ultima ruota del carro" which means "the last wheel of the carriage". The last wheel is the spare wheel which happens to be the fifth.
I think "Third wheel" is best in English. Fifth wheel makes it sound more like a spare wheel for you car...
This can technically go as high as you want. I once referred to myself as the 17th wheel or something, because I was eating at a restaurant by myself and the rest of the tables were couples (and I counted them).
Third wheel of a bike or fifth wheel of a car. ☺
Although I do think that functioning tricycles are more common...
Should one always use the definite ending on a noun when one is describing it as first, third, fifth and so forth?
Preferrably, but not necessarily. You could say it in the indefinite, but then add the article too: Vi behöver ett femte hjul ("We need a fifth wheel").