Wow, that's an interesting question, and I hope that you will also get some input from some other Norwegians, as my opinion might not be very "representative"
I guess our perception of Swedish depends on the amount of exposure we've had to it, though. While most of us have definitely heard it a lot from music (a lot of Swedish bands/singers who sing in Swedish are very successful in Norway) or TV or children' popular culture (I remember watching things like "Pippi Longstocking" and "Emil from Lönneberga" in their original Swedish version when I was little), reading can be a different story. Most of my friends seem to prefer Danish to Swedish if they have to read anything in another Scandinavian language, but for me it's the other way around - I'm more used to Swedish, really.
I won't say that it looks like a "weird" version of Norwegian in any way, though. Rather, it looks like Swedish, and depending on what I'm trying to read, I might think of that fact or I might simply read without giving much thought to the fact that this is in fact a foreign language. For example, when doing normal everyday things like browsing the net or reading teletext, I don't actually consider reading in Swedish that different from reading in Norwegian, except if I spot a funny word or something where the meaning isn't obvious to me. On the other hand, reading a book can be more challenging, as there are likely to be more "peculiar" words there, and it's also a longer text so it makes me more aware of everything being in Swedish.
Does that help a little?
Native: [flag]no[/flag] Understand well, but will answer in Norwegian: [flag]sv[/flag] [flag]dk[/flag]
Using actively: [flag]en-US[/flag] [flag]es[/flag] Suffering from lack of attention: [flag]de[/flag] [flag]cs[/flag]
Want to learn one day: [flag]it[/flag] [flag]he[/flag] [flag]ja[/flag] [flag]ca[/flag] [flag]mt[/flag]