IP addresses are only visible to the moderators. If you're a mod, each post shows an IP address and there are logs you can dump. However, IP addresses are like post office return addresses...you can write in pretty much whatever you want by going through a proxy or an 'anonymizer' site.
The old moderator IP tools were pretty slick-- you clicked on a poster's name to get to their profile, and then there were two links to "check IPs". I forget the names of the two links but one listed all the IPs that poster had ever used, and another listed all the posters who'd ever used a specific IP. So you could check both names & IP addresses. IIRC you could also see what IP addresses they'd used for their last dozen or so posts and whether or not there had been any login errors.
I haven't used these IP tools much (they're much more awkward, requiring a second login and a lot of keystrokes) but I can't ever recall anyone other than CFB using a proxy router. Some posters would have literally dozens of IP addresses from using dialup, others would have two or three from switching among work/home/travel, some would only have one.
It's not rocket science and the IP address wasn't usually the first sign. Moderator antenna would twitch when a poster reminded a moderator of someone else. It'd be similar vocabulary or sentence structure or a certain subject or wading right into another poster without seeming to need to get acquainted first. A very first post jumping into a subject without any sort of introduction might be a tipoff too. (The same frequently applied to spammers.) So by the time a moderator found one IP address with two user names there was never any doubt. We'd post our findings to the moderator's section of the board and talk about what, if anything, needed to be done.
If I remember someone using multiple IDs when I was a moderator, and if it looks like it's happening again, then I'm going to call moderator attention to it. If it looks like two posters are suspiciously similar in nature then I'm going to call moderator attention to it. And if it's spam, then I'm going to... you get the point. But I'll also let you know what I think you're doing.
If I'm not responding directly to your posts then it's probably because you're on my "Ignore Poster" list. But if it's really important to you to get my attention then feel free to send me a PM. Or forward your complaints to a moderator, and I'm sure things will get worked out!
Having said that, I won't be on the board much between now and the 26th.