How did "stroke" become the verb "strike" to mean "deal a blow"?

etymology meaning old-english middle-english

I suspect that John Lawler's comment is the key to this question. The earliest use of "strike" in this sense in the OED refers to being struck by a weapon. As noted in the aforementioned comment, passing over something with a weapon carries an inherent implication of violence, which probably stuck with this sense of "strike" until it became as common as it is today.

The earliest cited use is from 1377

Al-þough þow stryke me with þi staffe with stikke or with ȝerde.

  • 1377 - Langland Piers Plowman B. xii. 14

The OED offers no specific etymological notes for this sense beyond what has been outlined in the question, so this explanation for the sense related to hitting something is somewhat speculative.

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