しまう、きる、 and ぬく are more or less similar, but there are subtle differences.
しまう: I assume you mean definition 6ア in the link, or definition 4. in Jisho. しまう puts more emphasis on the end state than the actor or action, being a word that signifies the end of a state transition. (Those familiar with Chinese will find that しまう having an (admittedly rare) alternative kanji reading of 了う should see a connection.) See these example phrases in the dictionary entry:
- 「[早]{はや}く[食]{た}べてしまいなさい」: The speaker is ordering a transition from the food being not eaten to the food being eaten (with an implicit subject of the 2nd person).
- 「あきれてしまう」: The speaker is describing a transition from not being あきれている to being あきれている (with an implicit subject of the 1st person). The adjective is tricky to translate but means something like a combination of bewilderment and dismay. Or "the facepalm feeling," whichever you prefer.
ぬく、きる: See Difference in usage of きる and ぬく attached to verb 連用形
With regards to ぬく, my particular online dictionary doesn't mention if 貫く is a proper spelling when attached to a verb's 連用形. It does say that 抜く is correct. (Definition 15)
That being said, I can attest that the definition where 貫く is considered correct, Definition 10 ("To pass through to the other side, to connect one place to another"), is the nuance given by adding ぬく to a verb's 連用形. We essentially want to break through a metaphorical wall that stands between the "action is not complete" state and the "action is complete" state, and ぬく is the verb by which we punch through the wall to the "other side."
If there are similar verbs/suffixes
>> やりとおす やりとげる やりつくす とかですかね・・・ – Chocolate♦ Apr 8 '17 at 16:59