Reason behind Oxford Dictionaries's IPA transcription?

Solution 1:

It's just an alternative transcription for the same phoneme that you and Wiktionary transcribe as /aɪ/ (the vowel found in the words "price" and "size"). Oxford Dictionaries' transcriptions do not use the symbol aɪ, so there is no contrast between ʌɪ and aɪ. The use of ʌɪ in this context is unrelated to "Canadian raising".

Oxford consulted the linguist Clive Upton for its transcriptions, but Upton's choice of the symbol ʌɪ was criticized by the linguist John Wells for reasons that Wells explains on the following web page: IPA transcription systems for English. Not all linguists use IPA the same way.

It isn't very easy to nail down the use of the various IPA symbols for "a-like" vowels such as /æ/, /a/, /ɑ/, /ɐ/, /ʌ/, /ə/, /ɜ/. English is unusual in having a relatively high number of contrastive vowel phonemes in this area but different accents, and even just different individuals, pronounce things differently. When two IPA symbols are used together to represent a diphthong phoneme, it doesn't necessarily mean that the diphthong is pronounced exactly like a combination of the distinct vowel phonemes that the IPA symbols represent when used separately. So you shouldn't be too surprised by the discrepancy between the sound that you use at the start of /ʌɪ/ and the sound at the start of the word under.