You haven't said what denomination the family was. However looking at the 1901 Irish census for Co. Armagh all Hodgens were Church of Ireland (ie Anglican) so I'll assume your family were too.
Portadown is in the parish of Drumcree. There is a church in Drumcree and another in Portadown itself (St Marks). St Mark's only has records from 1826 which I suspect is when it opened. Drumcree has baptisms from 1788, marriages from 1802 & burials from 1804. I would suggest you search the Drumcree records for Deborah & James baptisms (and that of any siblings). Tradition was to marry in the bride's church so you may also find Deborah's marriage there. Probably just before they left Ireland.
These church records are not on-line anywhere so far as I am aware. There is a copy in PRONI (the public record office) in Belfast.