I've found the following on the Dutch surname database of the Meertens Institute on Oosterom. It based on a placename, presently Oostrum. There are three places called that, one near Houten, province of Utrecht, one in Frisia and one in Limburg. Oostrum means Oosterheem : easternly situated settlement, as opposed to Westerheem/Westrum.
If you have any Dutch: more details on
http://www.meertens.knaw.nl/nfd/detail_naam.php?naam=Oosterom