William, I thought you were living in Vietnam; when did you move to India?
In AmE, you hear secondary stress on -ary; thanks to historical r neutralization, -ary becomes [eri]. Based on this and alternate stressing rule, you can find the other stressed location: /ɪkˈstroɚdəˌneri/ (note the stress on the second syllable left of the secondary stressed syllable. Also, notice the smoothing phenomenon: getting rid of the vowel /a/, and keeping /o/.
/ˌekstrəˈɔːdɪnri/ is possible, but it could be a marked usage in BrE. That's not part of AmE.
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