Over the years, I have heard 3 different ways to pronounce the word strength:
I definitely pronounce it with option 3 (shtrength /ʃtɹɛŋθ/), starting the word with an /ʃ/ ("sh").
For me, option 2 (strenth /st̠͡ɹ̠ɛn̪θ/) sounds too simplified as there is not even an ŋ, although I have heard others say it that way.
I am curious about option 1: /stɹɛŋkθ/. I am having trouble hearing (and saying) the very soft k that is being inserted after the /ŋ/ and before the /θ/. Do people still pronounce the word this way, or is it more often pronounced as option 2 or 3?
My apologies. I read the question too quickly, and did not notice the question was about the pronunciation of the "k". My previous answer was in regards to the "sh" sound in your third example. Shtrength is incorrect pronunciation. Only "sh" in a first syllable makes the "sh" sound in English. In a second syllable, "ci", "ti", and "si" can also make the "sh" sound. The "str" in strength should be pronounced like the "str" in street.
Regarding the pronunciation of strength...such an interesting question. The correct pronunciation is your third example (minus the "sh"), as the "ng" in strength should be pronounced like the "ng" in hung, which is formed by placing the tongue back in the throat. Then followed by the "th" as in "three", which is formed by placing the tongue between the teeth. Perhaps it is all this tongue moving..lol..or two soft phonograms next to each other that causes a US speaker to add a hard "k" to make the pronunciation easier. It is incorrect pronunciation, but I use it myself. So minus the "sh", #3 is how strength SHOULD be pronounced. #1 is how it is USUALLY pronounced (as it is easier on the lazy tongue). Occasionally I hear #2 - it may be a British pronunciation, and that is what it sounds like to the American ear.
Asking about “strength” is a big question because you’re really asking about two fairly distinct pronounciation issues: the pronunciation of “ength” and the pronunciation of “str”. People mostly pronounced strength in a way that rhymes with length and alliterates with string or stream.