avoiding an oncoming vehicle -- what is the specific term for this in English?
Solution 1:
Swerve is the word most would use if the action is immediate and reactive. It means to turn immediately out of the way, and it describes the jerky action you would likely make in that situation.
I swerved to avoid the pedestrian who darted into the road.
If it were a simple changing of lanes, you would just say change lanes.
Solution 2:
To provide an alternative, the first word that pops to mind for me is "dodge".
I dodged the oncoming car just in time!