No, it does not sound weird. It sounds perfectly normal, but you would probably assume that the person is either uneducated, or is a song-writer, or a novelist constructing some dialogue. Lots of people use non-standard constructions. They would not consider them incorrect, even if the grammar books do! It's common to hear forms such as "He were coming along the road when...." or "I were watching TV when...." or "Was you late for work?" Is you happy with this answer?

It doesn't sound weird, but it does sound uneducated if a person says this in the real world. In fact, millions of native speakers do use this construction - it's a kind of dialect form, like 'I ain't got no money'. Some people talk like this because they genuinely don't know the correct grammar, while others do so to be accepted by a particular social group. And you're right about the poetic licence. A song-writer can get away with these non-standard forms, because in many cases (again, like 'ain't), they can actually sound better than the correct forms when sung.

imho, it would be the native speakers that find it LESS strange, as they tend to be the most comfortable and loose with their slang. I think it's we language learners and teachers that fixate more on what's grammatically or morphologically appropriate because it's always a conscious part of our learning process, even during casual conversation, or so I feel. But hey, if the oxford dictionary was written by a few old prescriptive white-as-white-can-be British gentlemen who now occupy a minuscule fraction of the native English speaking world, who's to say that, say, African or South American slang is only appropriate under poetic license? Maybe you only earn the right to break the "rules" of your language once you've actually learned them properly, but I root for desciptivists myself so meh, whatever gets your point across, right? And conversely, if your language deviates so far from the norm that you can't even be understood by native speakers that's where language defeats its own purpose lol. If slang helps some people express themselves better, I don't see much harm in it as long as it doesn't misinform language learners. I don't think it's weird, just a bit annoying. pardon my chronic ramblinnnngggg~~~ - "♪ We don't need no education ♪" - "Yes, you do. You've just used a double negative."

Don't rely on songs to contain correct grammar, there is poetic licence to use colloquialisms and non-standard forms because it fits the music better. I saw a post yesterday asking about the song 'Ain't No Sunshine' by Bill Withers. Again it isn't correct grammatically, but it sounds much better musically. Anyway it doesn't sound weird to me, even in spite of the fact it's grammatically wrong.

You're correct in saying the grammar is incorrect, but it's not weird at all, it's fairly common. Thinking about where it's come from, I wonder whether it's because 'you don't know me' is in that format and people being lazy or making a mistake have copied that.