This explanation goes for rhotic varieties of English, including General American (and Canadian) English. Forget about spelling — English spelling is etymological, not phonetic. “War”, although spelled with “a”, is pronounced with the open-O sound: /wɔr/. “Word” and “world” are absolutely *not* pronounced with any sort of “o” sound whatsoever. They are spelled with “o” for historical reasons, but *there is no “o”.* That is the why you’re mispronouncing them. “Word” rhymes with “bird”, “curd”, “heard”, and “herd”. There is no “o” — just pronounce the “r” as if it were the vowel. Yes, the “r” can be a stressed vowel in American English. “World” is the same as “word”, except that you need to pronounce “l” between the “r” and the “d”. Let me know how it goes!

War is pronounced more like "wor". To pronounce "world", try raising your tongue to the roof of your mouth after saying "wor". Hope this helps.

Pull your tongue back after the R and before the L. Like woReLd. Practice that a couple times and then say it faster.