When talking about addresses:
'in' is used to suggest an address ('I live in Kennington Road.')
'on' is used to suggest the general location of a larger or very well known place, like a attraction or even a city. ('Greenville is on Highway 57.')
If you are talking about something that is placed on the road, normally both AmE and BrE would use 'in'.
'She's walking in the street!'
'Watch out! There is a tire in the road.'
They drink 'in the street' because they are there temporarily.
The pub, a fixture in the locality, is 'on the street'.