OLE object (embedded image object) in a body of a Discussion Board cannot be migrated from SharePoint 2010 to Office365 SharePoint Online . No errors logged.
And, it is vice versa - OLE objects are not migrated from Office365 SharePoint Online to SharePoint2010.
It is not possible to migrate from a Sharepoint 2010 to a different Sharepoint 2010.
OLE (embedded image object) object is not getting migrated as part of a discussion board because OLE object in discussion board is not treated as migration target item.
It is not possible to migrate OLE objects using the tool by design.
As workaround, locate and save image(OLE object) on source environment in advance. Then, upload it individually to target after the migration.