This is a pretty well-known area of variance among different North American accents of English. It's certainly not unique to you. In this post, I'll use the spelling "ohr" /or/ to represent the sound in in sore, and "ahr" /ɑr/ to represent the sound in star.
However, there are added complications in that some people may distinguish three vowels among glory, sorry, and starry (they are all different in standard British English, for example). So I'll start out by outlining these, and then describe how these vowels area merged in various North American accents.
Accents with a three-way distinction
In British English, words like glory are pronounced with /ɔː/ (the vowel in law), words like sorry are pronounced with /ɒ/ (the vowel in lot), and words like starry are pronounced with /ɑː/ (the vowel in spa).
Usually, Canadian English speakers shift the vowel in lot to /ɑː/, but there is an exception before /r/. So they generally do not shift the vowel in sorry to /ɑː/ Most transcriptions I've found give the vowel in "sorry" as /ɔ/ or /o/; despite this, it seems that some Canadian English speakers still maintain a contrast between the vowels in sorry and glory (with a higher, tenser or longer vowel in the latter word), although both vowels may be shifted a bit compared to British English.
Accents where horrible = hahr-ibble
Accents like yours, where words like sorry and horrible are both pronounced with /ɑr/, are described in this blog post: The Oral-Aural Merger?, by Neal Whitman. Whitman says he sent a message to the American Dialect Society email list asking about dialects like this, and got several responses. Ben Zimmer said that areas where this pronunciation is common include New York City, Philadelphia and the Carolinas.
In 1944, it seems the "ahr" pronunciation was associated with Eastern-Southern American speakers, and the "ohr" pronunciation was associated with Western speakers, according to the research of Charles K. Thomas of Cornell (American Language Supplement 2, H.L. Mencken).
In some accents, even more words have /ɑr/: for speakers with the card-cord merger, words in the "north" lexical set are also pronounced with /ɑr/. These speakers only use /or/ in words like "glory" and "hoarse" that historically had long vowels (this is mentioned by one of the mailing list replies by Matthew J Gordon). (For a longer explanation of the distinction between "north" and "force" lexical sets, see my answer here: Why is 'forty' spelled without a 'u' in Canadian/British English?)
Accents where horrible = hohr-ibble, but sorry = sahr-y
For many other speakers in North America, the vowel in words like horrible has merged in another direction: with the vowel of glory. American English speakers with this merger, like me, say "ohr-ange, hohr-ible," etc. Interestingly, though, this change does not apply in all words: we also say "sahr-ry, sahr-roh, to-mahr-row." That is, we split this set of words into two new sets. Here's a relevant question about this: Where did "sorry" get its vowel sound?
There's a description of this split in this Wikipedia article: North American English Regional Phonology - General American. Apparently, the "ahr" set includes, at a minimum, the four words borrow, tomorrow, sorry, and sorrow. It says more words may be pronounced with "ahr" in the accents of speakers from New York, New Jersey, Philadelphia, and the Carolinas.
Not everybody agrees about which words fall in which set. Based on your described pronunciation of historic and exploratory with "ohr" rather than "ahr," it seems like you actually have a split as well, just a different one from your friends where more words are in the "ahr" set.
The Language Samples Project site that I linked to earlier for the description of Canadian English actually gives two lists. For words pronounced as /ɑr/ by nearly all General American speakers, it gives sorry, tomorrow, borrow, sorrow, and additionally Laura. (In fact, this doesn't seem to be entirely accurate. I pronounce Laura with "ohr," and Peter Shor agrees that this is the most common pronunciation outside of New York.) For words variably pronounced as /ɑr/ by General American speakers (but more commonly pronounced as /or/), it gives Florida, orange, oracle, Norwich, adorable, thesaurus. You pronounce "horrible" with /ɑr/, even though it's not on the second list. In fact, according to Wikipedia and Merriam Webster, the set of words that may be pronounced with /ɑr/ is much more extensive than either of these lists, and seems to potentially include any word that historically had /ɒr/; for example, it lists alternate pronunciations with "ahr" for florist, forest and historic. The sound in words like florist has been discussed on John Wells's phonetic blog (forceful sports supporters), and although he mainly focuses on British pronunciation, there are some interesting comments about variations in American pronunciation.
Best Answer
Dutch /u/ is not necessarily the same as English /u/.
I think you may be confusing the concepts of "phoneme" (which corresponds to the adjective "phonemic") and "phone" (which corresponds to the adjective "phonetic").
A phonetic transcription, using square brackets, represents a specific physical sound. When comparing sounds from different languages, you want to use a phonetic (bracketed) transcription.
But, Wiktionary transcriptions are not phonetic. They are phonemic. (They may also have other complications, like inconsistent systems being used for different words.)
A phonemic transcription, using slashes, like /ˈfju/, doesn't directly represent the sounds coming out of someone's mouth. It represents the minimum amount of information a native speaker needs to know in order to pronounce a word correctly; the important sound contrasts in that specific language. As a non-native speaker, you can't rely on a phonemic transcription to tell you pronunciation details.
Unlike French or Dutch, the English sound system does not distinguish between the phonetic sounds [u], [y] and [yu̯]. Some speakers may very well have a phonetic [yu̯] or something similar in "few", but it is still considered by English speakers to be the same sound as in "fool" where a phonetic [u] would be more common.
The realization of the English phoneme /u/ as the phone [y] or [yu̯] is considered a type of fronting, moving a vowel sound to be pronounced further forward in the mouth.
This fronting of /u/ common in North American varieties of English, especially when /u/ comes after the palatal glide /j/ or one of the coronal consonants /n, t, d, tʃ, dʒ, s, z, ʃ, ʒ/. (I think l might also be included in this list, but I'm not sure.) You can find an illustration of where this type of fronting is common at the Atlas of North American English. The fronting is least common when /u/ is preceded by a non-coronal consonant and followed directly by /l/.
The linguist Geoff Lindsey has made some blog posts mentioning the existence of this front realization of /uː/ in "Standard Southern British", and the tendency to use a more back realization before "dark l".