strain (v.) Look up strain at Dictionary.com
c.1300, "tie, bind, fasten, gird," from present participle stem of Old French estreindre "bind tightly, clasp, squeeze," from Latin stringere (2) "draw tight, bind tight, compress, press together," from PIE root *streig- "to stroke, rub, press" (cognates: Lithuanian stregti "congeal, freeze, become stiff;" Greek strangein "twist;" Old High German strician "mends nets;" Old English streccian "to stretch;" German stramm, Dutch stram "stiff").

From late 14c. as "tighten; make taut," also "exert oneself; overexert (a body part)," Sense of "press through a filter, put (a liquid) through a strainer" is from early 14c. (implied in strainer); that of "to stress beyond measure, carry too far, make a forced interpretation of" is from mid-15c. Related: Strained; straining.
strain (n.2) Look up strain at Dictionary.com
"line of descent, lineage, breed, ancestry," c.1200, from Old English strion, streon "a gain, acquisition, treasure; a begetting, procreation," from Proto-Germanic *streu-nam- "to pile up," from PIE root *stere- "to spread, extend, stretch out" (see structure (n.)). Hence "race, stock, line" (early 14c.). Applied to animal species from c.1600; usually involving fairly minor variations, but not distinct from breed (n.). Normal sound development would have yielded *streen, but the word was altered in late Middle English, apparently by influence of strain (n.1).
strain (n.1) Look up strain at Dictionary.com
"injury caused by straining," c.1400, from strain (v.). The meaning "passage of music" (1570s) probably developed from a verbal sense of "to tighten" the voice, which originally was used in reference to the strings of a musical instrument (late 14c.).