The one essential quality that defined a demigod, or hēmitheos, in antiquity was having half-divine parentage. There are no other generic qualities, and certainly no hint that I'm aware of of particular odours.

The earliest appearances of the word don't give much of a clue -- Homer, Iliad 12.23 and Hesiod, Works and days 160 -- but various later appearances of the word do. A fragment of Simonides refers to (523.1-2)

they who came before, the hēmitheoi who were sons from the lord gods

and Plato makes the meaning more explicit (Kratylos 398c-d):

'Do you not know that the heroes are hēmitheoi?'

'Say what?'

'All those that were born from the love of a male god and a female mortal, or a female god and a male mortal?'

The only secondary characteristic is that the word is adopted as the standard word for the heroic figures in legends of the 'heroic age'. M. L. West's commentary on the word in the Works and days cites a bunch of appearances of the word, then comments,

As the examples quoted show, the word refers to their parentage (cf. ἡμίονος ['mule', lit. 'half-ass'], and our 'half brother'), not to semi-divine status. It, not ἥρωες, is the word used in speaking collectively of the men of the heroic age; and it is noteworthy that in Homer it is only admitted in a passage where that age is viewed from the distance of the poet's own time ...

The meaning of hērōs (the origin of the word 'hero') is more about contemporary religion rather than legend: it gets used in connection with cult-sites of the 'present' day devoted to a particular hero, rather than to characters in legendary tales.

So, to sum up:

1. Defining characteristic: half-divine parentage.
2. Secondary characteristic: hēmitheos is the word typically used to refer to legendary 'heroes'.