Effects:
After brainstorming ideas outside of basic RP (Declaring wars and such simply because you hate the other guy,) effects would range from political to personal. An example of political would be: Duke is of House Bedwyr, Lord within duchy is of House Norrel. House Bedwyr has recently declared House Norrel to be in complete and utter disfavor. As such, and for some strange reason, extra taxes (not too much, or abuse would be a huge problem) would be collected.
Example of personal: House Octavius has slandered House Penardin. Both set standings to hatred. The specific incident was between Selene and Mathilda, and they decide to duel it out. If it is to the surrender, a larger chance of a critical wound or even death should be present. If it is a duel to the death, a significant increase to probability of death should be present. This could branch into say "Healers drag Mathilda away, as she is severely wounded, but Selene chases her and cuts her down. Selene is arrested by the authorities who were nearby, and is currently rotting in your cells."
Though I understand actually killing characters is something we should keep in low doses, it makes sense to me that hatred and blood feuds would incur that kind of irrational behavior.
Maybe have it drag into the army and its cohesion. Bedwyr is Marshal, Norrel is an archer unit. The enemy approaches, Bedwyr gives the order to fire (auto fire as it is in range.) Norrel's unit does not fire until the enemy is doubly closer. (Have the report say "Norrel Archers did not fire as a result of unforeseen circumstances.") Your army takes a few extra loses, but wins regardless. Bedwyr is pissed, Norrel is satisfied to have pissed him off, but faces the potential consequences.
The above gives the potential to drag more houses into the feud.
For positive traits, maybe flip the situation over (positive standings = tax breaks, Archers have increased morale, etc..)