I'll point out your phonetic note is a bit restrictive; for one thing, "orange" isn't necessarily even two syllables (at least not in General American). I personally would say I only rarely enunciate it as two separate syllables. "Orange" also can use the ĭ vowel like "hinge" when it's two syllables, although of course when it's a polysyllabic word it's stressed on the first syllable so "hinge" is not sufficient. "Door hinge" does rhyme within the range of pronunciation of "orange" in General American, even though you're more likely to hear either " ôrənj" or " ôrnj," and check Wiktionary if you don't believe me (although I can't say I believe its claim of "ôrənch"; that's just crazy).



But of course, the "nj" sequence isn't exactly common in English (I wonder if one day we'll lose it entirely and start saying things like "hĭng"), so it's no wonder that a word with several valid pronunciations ending in such a weird sound has a reputation for not rhyming.



Also, I can't believe you got me to use enPR for this entire comment. IPA forever, down with enPR!