For me both 'talk to' and 'speak to' are the usual neutral forms meaning 'address' and 'converse with', though both also have an additional pregnant sense 'rebuke, buttonhole, dress down'.

As to 'talk with' and 'speak with', I could use these, and don't feel they're Americanisms, but they're much less usual. 'Talk with' is associated with Dr Doolittle, where it was required as a parallel to 'walk with'. The 'with' forms are largely absent from my dictionaries.

There was a comedy episode, of what I can't remember, where a German tourist said 'talk' and a choleric Arthur Lowe snapped 'Parrots talk, people speak!'.