/ˈɛːrɪən/ is just an Anglicized pronunciation of “Aryan”. I’m not sure how old it is, but it is fairly easy to explain based on English phonological and orthographical tendencies.
In a number of varieties of English, the sequence /rj/ does not exist; and even in the ones where it is possible, there seems to be a tendency to avoid it whenever possible via a “conspiracy” of sound changes that turn it to something else.
When the /r/ is not preceded by a vowel, the sequence /rj/ has been eliminated in the great majority of English accents, including standard British and American English, by deleting the /j/. Words like “rue” and “true” are standardly pronounced like “roo” and “troo” rather than “ryoo” and “tryoo”. This is one example of a broader phenomenon called “yod-dropping”.
When the /r/ is preceded by a vowel, some accents do tolerate the sequence /rj/, but many accents avoid it in various ways. For example, /j/ is often simply dropped in words spelled with a vowel followed by “ru” such as ferrule, erudite, querulous. In words spelled with a vowel followed by “ri”, the “i” is often pronounced as an independent syllable rather than as a glide, such as carrion, material, inferior. (There are also a few words spelled with "ri" where the “i” is simply silent: carriage, marriage.) In general, the letter “y” acts exactly the same as the letter “i” in the middle of a word: see embryo and eukaryote.
There are some words with /j/ that cannot be dropped or syllabified, such as compounds like lumberyard. In standard British English, words like this don’t have /rj/ because the sound /r/ has been dropped: /lʌmbəjɑːd/. In standard American English, this is a case where /rj/ seems to be necessary, but it’s not a common situation at all. If there is any real difference between British and American use of /rj/ in the word Aryan, I would guess this is part of the reason for it: Americans can conceptualize it as being pronounced like a hypothetical compound word “ar-yan”, while this doesn’t really work for a non-rhotic British English speaker.
In terms of etymology, the OED says
[the spelling] Arian has long been in English use: Aryan is of recent introduction in Comparative Philology, and is also by many written Arian, on the ground that āria was the original word, as shown by the Vedic language, ārya being only the later Sanskrit form
but I imagine only a tiny fraction of people base their pronounciation of this word on this consideration.
The pronunciation of the vowel as /ɛː~eə~e/ is just based on the usual English value for “long a” before r. As far as I know, there is no significant phonological reason in English for /ɛː/ to be preferred over /ɑː/ here, but spelling often has a strong influence on the pronunciation of loanwords (all literate English speakers are exposed to the English spelling system regularly, while few of them are ever exposed to Sanskrit pronunciation), and /ɛː/ is more regular than /ɑː/ within the system of English spelling.
German pronunciation is somewhat irrelevant because “Aryan” is not a word in German: the German word is “arisch”, and it's pronounced with /aː/, which is simply the usual “long” pronunciation associated with the letter “a” in German.
I have never heard of people using different pronunciations in "Aryan" and "Indo-Aryan".