The word "strain" originates from the Middle English streinen (c1300), meaning "to bind, tie, or fasten".  It derives from the Old French estreindre and ultimately from the Latin stringere, meaning "to draw tight, bind tight, or compress".  It is related to the root strict and implies tension, pressure, or overexertion.  As a noun, strain refers to pressure, tension, a severe, taxing effort, or a, type/breed (e.g., of virus). As a verb, it means to pull tightly, overexert, injure a muscle, or filter a liquid.   A separate, earlier, and unrelated sense of "strain" (meaning pedigree, race, or lineage) originates from the Old English strēon, which refers to gain or acquisition. 

According to the Oxford English Dictionary (OED), the earliest known use of the word strain varies depending on whether it is used as a noun or a verb, with its roots in Middle English (1150–1500) and Old English.  Noun (injury/tension): The OED records this sense starting later, with early evidence from the 1550s or 1580s.  Noun (line of descent/breed): The earliest evidence for this sense of "strain" is from the Middle English period, specifically recorded as early as the 13th century or early 14th century (c. 1300–1400).  Verb (to bind/tighten): Recorded from the Middle English period, with instances cited around 1300–1532.  Verb (to exert/stretch): Recorded from the Middle English period, with evidence as early as the mid-1400s.

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STRAIN Definition & Meaning - Merriam-Webster

STRAIN Synonyms: 441 Similar and Opposite Words | Merriam-Webster Thesaurus