Now that Chekhov has posted her terrific solution of the case, I would like to focus more on the different rooms and movements of important characters. There honestly has been little to no discussion about whose room is whose, so I will try my best to elaborate on it. Basically, I will say what room fits best with what character and why. But I will warn you, it will be difficult to follow what I'm saying if you don't know what's going on.
NOTE: When I say something like 821.12.8, I'm referring to FILE#.PAGE#.PANEL#
Scar Akai's Room: <7B
In File 818, the Detective Boys try to chase down the "pretend culprit" by heading away from Car 7 (towards a Car # that is less than 7). After realizing that the Deduction Quiz hasn't started yet, Conan heads back towards Car 7 while Haibara sees Scar Akai exiting the second room from the back, (818.13.6 & 818.14.1). Therefore, Scar Akai's room is <7B. The room is most likely not 6B since Conan didn't feel like he miscounted the number of CARS (818.15.5), which would suggest that he passed through more than one car when getting from the car SA was seen in to Car 7. So SA's room could be 5B, 4B, or 3B as well.
Okiya & Mysterious Lady's Room: 6E
In File 820 after Conan tells the DB, Ran, and Sonoko to stay in their room (820.3.7 & 820.4.1), they follow Conan's order and head towards Car 7. However, it gets a little tricky on the next page because we do not know whether the gang is in Car 7 or Car 6, nor do we know if they're heading towards Ran and Sonoko's room in 7B or the DB's room in 6D (820.5). I will assume they are in Car 6 for now and I will explain why later. So after Scar Akai passes the gang by walking towards Car 7, we see Amuro talking with Ran outside of Room 6E (820.6). Since we see Okiya peeking behind the door, we can assume that Okiya and the mysterious woman's room is 6E. But why 6E and not 7E you ask? If the gang were in Car 7 while talking to Amuro, that means Scar Akai would be heading towards Car 8. That wouldn't make sense because Conan, Sera, and Kogoro are still investigating the case in Car 8. So it's safe to assume that the gang is heading towards the DB's room in 6D (there is a contradiction about this that I will explain later) and that Okiya and the mysterious woman's room is 6E.
Amuro's Room: 7A
In File 821 after Conan appears to have solved the case in Car 8, Sera heads towards Car 6 to confirm things with the DB (821.14.2). In Panels 4 and 5, we can assume that Sera is running through Car 7 since Kogoro and Conan are no longer seen behind her. As Sera passes through the corridor, we can see Amuro peeking out of either Room 7A or 7B, but it's obviously not 7B since that would be Ran & Sonoko's "new" room (previously Murobashi's room before the switch-up). Therefore, Amuro's room is 7A.
Random Man's Room: <7C
In File 819, the DB try to inform the conductor (that was seen in the same car as Scar Akai) about the missing Car 7. After he tells them that they are mistaken, the light signal and bell above Room C go off and a man with glasses and a moustache (maybe a person in disguise?) is seen opening the door (819.3.6). So like Scar Akai, the random man is staying in a Car # that is less than 7, or in other words, Room <7C. As for the man's identity, I would like to speculate that he is Yusaku in disguise (which would confirm the speculation that Yukiko is the mysterious woman in disguise), but the man is probably not significant in the plot at all. Just in case he turns out to be an important character later on, I wanted to toss around the idea.
Other Justifications
-In File 821 before Sera enters Car 6 to confirm things with the DB, Scar Akai and the mysterious woman pass by each other in Car 6 (821.15). By looking at the positions where they were standing in Panel 1, it justifies that Scar Akai exited his room and that the woman exited her room before they crossed paths (assuming that Scar Akai's room is 6B).
-In both 820.6 and 821.15, Scar Akai is seen walking towards Car 7. This not only justifies that his room is <7B, but it also justifies that Amuro's room is 7A (if we assume that Amuro's room is where Scar Akai intended to go to both times).
A Gosho Mistake?
In File 821, the Detective Boys, Agasa, Ran, and Sonoko are in what should have been Room 6D (since Conan specifically ordered the DB to "return to your room with Ran"). However, after Haibara receives a text message from Vermouth and exits the room, Ran goes after Haibara and during which, we are able to see the "B" emblem outside the door (821.6.7). But wait, isn't the DB's room supposed to be 6D? The snacks from before behind Agasa are still inside the room (821.5.5), so did Gosho make a mistake? The room that they're in cannot be 7B for many reasons. Like I mentioned before, the gang was hanging out in the Car 6 corridor when they first saw Amuro because it wouldn't make sense if Scar Akai was heading towards Car 8 when there was an investigation occuring (that's why it makes sense that Scar Akai was actually heading towards Amuro's room in 7A). Additionally, after Haibara saw Okiya opening the door that led from one car to another (821.9), she entered through the door, so it would only make sense that she went from Car 6 to Car 7, not from Car 7 to Car 8, because the investigation in Car 8 was still going on. Therefore, the gang was actually in Room 6B in File 821, which totally contradicts several things that I have noted. That's why I think it's possible that Gosho had made a huge mistake and had forgotten that the DB's room is 6D instead of 6B.
CHEK, I NEED YOUR TAKE ON ALL OF THIS
Looks good and logical to me. Scar Akai's room could be lower than 6B, but chances are he would want to be close to everyone else, so 6B isn't a bad guess. Today's mod power abuse is brought to you by Chekhov
EDIT: I changed Scar Akai's room from 6B to <7B and the random man's room from 6C to <7C (the number of cars the DB ran through wasn't ever clarified).