International Phonetic Alphabet

Merriam-Webster, which you link to, doesn't use IPA. (Its learner's dictionary does, though.)

Lexico, Cambridge and Collins use IPA - although if you use Lexico's US edition then it gives two transcriptions for each pronunciation, one IPA and the other non-IPA. (Lexico's UK dictionary uses IPA only.)

Lexico has two pronunciations of "entail": /ɪnˈteɪl/ and /ɛnˈteɪl/. This reflects the fact that both are valid pronunciations and different people pronounce it differently - although you should not rely on dictionaries to specify all the valid pronunciations.

Cambridge has /ɪnˈteɪl/, and Collins again /ɪnˈteɪl/.

What do you mean by "strict IPA"? Dictionaries generally use phonemic transcriptions rather than phonetic ones.

Apart from the fact that there are sometimes multiple valid pronunciations, you will sometimes notice different phonemic transcriptions even of (British) Received Pronunciation. For example, Lexico has /bɛt/ for "bet", whereas Cambridge has /bet/. These differences are systematic and deliberate.

John Wells has described the difference between the two schemes: "This hard-won uniformity was shaken, however, by Clive Upton's appointment as pronunciation consultant for Oxford's native-speaker dictionaries. His scheme, adopted by the influential Concise Oxford Dictionary (1995) remains quantitative-qualitative, but differs from the standard scheme in the symbolization of five vowels."

So the vowel that was traditionally transcribed /e/ became /ɛ/ in Upton's scheme (and thus in Oxford dictionaries and in Lexico). And there are similar differences for other vowels.

The transcription is still IPA and is still phonemic. It is simply an alternative choice of vowel symbols to represent those phonemes. You can argue which one is better or worse (Wells largely favours the older system: "In at least some of the cases one can see what motivated Upton to alter the standard symbol: but in my view the supposed gains did not make up for the sacrifice of an agreed standard").