This problem has different solutions depending on how you want to play.
If you're just looking for the achievement, one solution to your problem is to do whatever missions you want, choosing the side of good, until you get relatively close to your level point. Then go into a town and steal (for minor karmic reduction) or lay waste to entire towns (for major karmic reduction). You can quickly lower your karma this way. Then, once you're neutral, go kill some random creatures until you level.
(If you're looking to steal, a good place to do it is at Dukov's place… he's got stuff everywhere.)
The "nice" thing about this system is that if you stay on the path of "good" the whole time, you can do this at each achievement point: be bad until you get to the right karmic level, level up, get your achievement, and then restore a save to get back to your good self. You can quickly get "good", "neutral", and "evil" achievements for all levels on one playthrough this way.
(I did this, because I don't really enjoy long-term playing as an evil character… but I do like my achievements!)
You could also do this as an evil or neutral character, but it's much easier to quickly drop from "good" down to your new goal, than to work your way up.
If you find that you're close to leveling, and you're at the right karmic level, and don't want to take a chance on changing your Karma by doing a story-type adventure, you can always go wandering looking for random bad people to take out. Going near the Washington Mall can get you some XP fairly quickly, and you can go inside the capitol building and clear out large areas without picking up any Karma, positive or negative.
Assuming you didn't change Xbox profiles or try to move game files to another account, Xbox Live doesn't store saved game information and would not have caused this problem. (Your Xbox profile still has FO3 achievements granted for those DLCs correct?)
It sounds like you either overwrote your saved game, or you loaded an older save file. If you never reset the clock on your Xbox after your move (and it won't be correct with no Internet on its own), then it might be loading the wrong saved game file as it probably uses the timestamps for "Continuing" your game.
Try looking at all of your FO3 saved game files to try to find one with your progress (or at least closer to where you left off).
Best Answer
The DLC is just scattered around the wasteland. In order to find the locations turn on your radio and you will see a bunch of new radio broadcasts. Listening to said broadcasts will make the DLC locations appear on your map (with the exception of Broken Steel). You can also go here and read the main article for each of the DLC's listed. The first quest in the main article has a "given by" section which will tell you how to access them:
As a side note when you reloaded the first disk after installing the dlc you should have gotten notifications that a new signal has appeared on your radio. So hopefully this isn't actually a bug.
The physical locations of the DLC (on your pc) are:
Just in case you want to check if they actually installed.