Hi,
OME gathers all the Asset Acquisition information from OMSA. If these information are fed in OMSA, OME will show it. It will be a good idea to check on the MN whether you are able to see the Asset information in OMSA. Also, as per my understanding these information are required to be fed once on the target server.
For the warranty status information, the details are fetched from the dell site using system service tag and you should be able to get the detailed information. For this, you need to have internet connection on the OME server. You can also set up Warranty expiration information. You can find detailed steps mentioned by Rob on en.community.dell.com/.../19515788.aspx