Does OPL have an online archive of obituaries published in the World Herald dating back to 1990 and, if so, how can one access it?
For obituaries since 1990, the first place to look is our Newsbank database, which provides online access (home access with Omaha Public Library card) to The Omaha World Herald (electronic content-HTML text, rather than appearing as it did on the newspaper page) going back to 4 Aug. 1983. Please note that full-text obituaries are available in this database only from November 1998, but you will find them indexed back to 1983; this at least gives you the date of the obituary so that you can find it in our microfilm collection--or request a scan via our research department ($5 fee).
Another good place to find an exact citation: The Greater Omaha Genealogical Society has produced a partial index of obituaries from Omaha newspapers. It's published at https://omahaobits.wordpress.com
An additional possibility is Legacy.com: http://www.legacy.com/obituaries/local There you can find obituaries from newspapers and funeral homes all around the country, including the Omaha World Herald--this site is best for fairly recent obituaries (last 10 years or so). I'm not sure of the earliest date you might find Omaha World Herald obituaries there, but it's easy to search.
Finally, if you are looking for an obituary from the African-American North Omaha community, you might find it in the Omaha Star; we have their digital database from 1938 to 2011, available full-text online (home access with an Omaha Public Library card).
I hope one of these solutions meets your need!
Martha Grenzeback/Main Library