Cannula is the Latin diminutive of the Latin "canna", or "cane". Cane is a plant or family of plants, much like a reed or bamboo; in English "a cane" is the stem of a cane plant. "A cane" has properties: It is long and narrow and hollow in the middle. And that's where we start from.

There is a cane which is a walking stick, not often made of cane, but "a cane" is good for more than just to lean on. "Canna" is a unit of Italian distance, and a canon is a ruler or measuring rod: In parallel there is a "rule" that you follow, which is the same word as a rule for measuring. A canon is a rule, axiom, or law; it is the rule (of conduct and worship) for a monastery, hence the book containing that rule; The Canon is the official list of whatever it is you're discussing, and a canon is a prebendary, an ecclesiastical figure who officiates in return for a benefice1.

The Spanish cañon or canyon opens out from the Spanish caña, a cane or reed, and it is hollow inside. The cannula the good doctor inserts into your vein is hollow too, but a cannel2 -- channel, or canal seems to have been open on top to begin with and only closed up when it became a conduit: Apparently it's not related. A cannon that thunders (formerly "canon") is long and hollow inside, and it is related, while "cant" is the unrelated "bent", but it does by chance happen to be as long and hollow as the rest. A canon loses its length in the OED's sense 14, where it becomes "a metal loop or 'ear' at the top of a bell, by which it is hung", and gains it back again in the cannular (but not canicular!) ornamental rolls on the ends of your breeches; these rolls are called canions.

Yes, and a candy cane comes from sugar cane in the factory, and from cane in the OED as well.

"Canoe" is from the New World and unrelated. A Menckenian "cannaille", a pack of dogs and by extension a rabble, is from the Latin "canis" or "dog", and is unrelated. The Gaelic "cannach" is cotton-grass, and is from something spelled "canna" by somebody, somewhere. It looks interesting, but the trail is cold . . . The "ch" is something a bit like the throat-clearing "ch" of modern Hebrew. I'm not so sure about Lucas Cranach. I think he's unrelated, too.

1 We'd all do well to have a benefice.

2 A cannel is also a candle with an elided 'd'.

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