"Getting on" and "getting off" are usually used to describe getting on or off of a freeway, highway, tollroad, or expressway. Historically, these major roads required more effort to get on or off than other roads did. For example, getting on or off a tollroad often requires visiting a tollbooth. Getting on or off a freeway (or other major highway) requires travelling in a special lane, and/or merging between lanes.

Your first and third examples involve ordinary roads ("Smith Ave." and "Jane St."). To my (American) ear, it sounds more natural to say "I turned onto Smith Avenue" than "I got onto Smith Avenue." (But it is still OK to say "I got onto Smith Avenue.") It would sound more natural to say "I got onto I-5" than "I turned onto I-5." (In this example, "I-5" is short for "Interstate Highway 5", which is a major freeway that runs north-south near the west coast of the United States.)

"I veered slightly to the left to avoid running over the chipmunk" sounds very natural. This means that you abruptly steered to the left, but only just enough to avoid the chipmunk. If you were trying to avoid something bigger, you might have simply "veered to the left to avoid the pothole", or "swerved to the left to avoid running into the deer."

"Getting on" and "getting off" are usually used to describe getting on or off of a freeway, highway, tollroad, or expressway. Historically, these major roads required more effort to get on or off than other roads did. For example, getting on or off a tollroad often requires visiting a tollbooth. Getting on or off a freeway (or other major highway) requires travelling in a special lane, and/or merging between lanes.

Your first and third examples involve ordinary roads ("Smith Ave." and "Jane St."). To my (American) ear, it sounds more natural to say "I turned onto Smith Avenue" than "I got onto Smith Avenue." (But it is still OK to say "I got onto Smith Avenue.") It would sound more natural to say "I got onto I-5" than "I turned onto I-5." (In this example, "I-5" is short for "Interstate Highway 5", which is a major freeway that runs north-south parallel to the west coast of the United States.)

"I veered slightly to the left to avoid running over the chipmunk" sounds very natural. This means that you abruptly steered to the left, but only just enough to avoid the chipmunk. If you were trying to avoid something bigger, you might have simply "veered to the left to avoid the pothole", or "swerved to the left to avoid running into the deer."

"Getting on" and "getting off" are usually used to describe getting on or off of a freeway, highway, tollroad, or expressway. Historically, these major roads required more effort to get on or off than other roads did. For example, getting on or off a tollroad often requires visiting a tollbooth. Getting on or off a freeway (or other major highway) requires travelling in a special lane, and/or merging between lanes.

"Getting on" and "getting off" are usually used to describe getting on or off of a freeway, highway, tollroad, or expressway. Historically, these major roads required more effort to get on or off than other roads did. For example, getting on or off a tollroad often requires visiting a tollbooth. Getting on or off a freeway (or other major highway) requires travelling in a special lane, and/or merging between lanes.

Your first and third examples involve ordinary roads ("Smith Ave." and "Jane St."). To my (American) ear, it sounds more natural to say "I turned onto Smith Avenue" than "I got onto Smith Avenue." (But it is still OK to say "I got onto Smith Avenue.") It would sound more natural to say "I got onto I-5" than "I turned onto I-5." (In this example, "I-5" is short for "Interstate Highway 5", which is a major freeway that runs north-south near the west coast of the United States.)

"I veered slightly to the left to avoid running over the chipmunk" sounds very natural. This means that you abruptly steered to the left, but only just enough to avoid the chipmunk. If you were trying to avoid something bigger, you might have simply "veered to the left to avoid the pothole", or "swerved to the left to avoid running into the deer."