In American English, 'on' would be used in your sentences -- and it would usually refer to a location that is on the side of the street. If you wanted to indicate that a person was standing in the middle of the street, you could use 'in' (AmE). I believe that the usage in British English may be a little different.
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KynIs "in" or "on" correct:In BrE, 'in' is used.
- The other day I saw him _ the street.
- I ran into him _ the street.