Hi
If there are problems in delivery, fires causing abandoned buildings, unhappy sims, low education or anything that generally can cause issues with your buildings and traffic, you can lose the Omega status and therefore lose the profits from the affected buildings. Also very important that your industry has zero unfulfilled freight orders. You need enough industry to supply all commercial with freight, so that the Omega-enhanced freight is being delivered to your commercial.
I don't know any way that you can be collecting profits from residential without having income from commercial and industrial. The factories are the first to convert, then then they will send Omega-enhanced freight to commercial buildings. It's the shoppers buying from Omega commercial buildings and returning home that are converting the residential to Omega. Double-check your Omega map - a red building means it's converted to Omega, and therefore you're getting profits from it. If you hover or click on a red building, the bottom part should tell you the profit you're receiving from that building.
If you're not opposed to watching videos, SkyeStorme's videos on building a full Omega city are packed with great tips and a full explanation of how Omega works. Each video is about 15 minutes long. I highly recommend them; they have a bunch of information that I've found very useful. I was never able to build a fully successful Omega city before watching them. Click on the spoiler tag for links:
Parts 1 - 5 show you how to build a base city with a traffic system that route the trucks from the Omega factories to all parts of the city. The city generates about $35,000 / hour
Part 1 - http://youtu.be/xjB2trc4758
Part 2 - http://youtu.be/256FeN86bkY
Part 3 - http://youtu.be/sRFOczKAH0U
Part 4 - http://youtu.be/4gHbXefrSGc
Part 5 - http://youtu.be/AMbQ4_QGLNw
Parts 6 - 9 show you how to add Omega to your city and include detailed explanations of exactly how Omega works. Every building converts to Omega, and it ends up with over $400,000 / hour Omega profits.
Part 6 - http://youtu.be/CbCj1_x0Xo0
Part 7 - http://youtu.be/7sTIfXaqtN4
Part 8 - http://youtu.be/gYjgIn4BRb4
Part 9 - http://youtu.be/1o6tbc7F8
If you're still having issues, reply back and maybe post a screenshot or two of your Omega map so I can see some detail in what you're missing. I hope this helps - Happy Building!