These two phrasal verbs are quite synonymous but there is a slight difference, and to intrude one's opinions isn't appropriate.
To intrude means interfering, so for example, asking too many questions to someone: this can become intruding.
To 'impose' is more than that: the person is now "forcing" the person to follow. Bob imposes his opinion on Mary by 'forcing' her to follow and accept his opinion ONLY. So here, Bob would tell Mary to think that ONLY Manchester is best and nothing else.
In summary, they are synonymous but to impose one's idea is stronger than just intruding. Also you cannot really say 'to intrude my opinion on someone else'.
Hope it helps
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