How does Over My Dead Bodies interact with combat-related abilities of creature cards in my graveyard?
During combat, all creatures in your graveyard are treated as if they were on the battlefield. Anything they could do at this time while they were alive, they can do now even though they are dead.
This is covered in the Unstable FAQAWASLFAQPAFTIDAWABIAJTBT:

Do the graveyard creatures cause attacking or blocking triggered abilities to trigger?
Yes. Remember that they're treated as permanents on the battlefield while in combat, so a graveyard creature attacking will cause anything that triggers when a creature attacks (including its own abilities) to trigger.

With further confirmation that &quot;on combat damage&quot; abilities work on Mark Rosewaters Blogatog

wretchedor30 asked: I have out Over My Dead Bodies and attack with Phage the Untouchable. As she is in a graveyard, would it still cause game loss, or is the ability only relevant on the field?
MR: Her ability still works.

In regards to your specific examples:

Raving Dead's ability triggers at the beginning of combat (which is during the combat phase), so you will need to attack a random player. If that player doesn't block Raving Dead (perhaps they have no creatures in their graveyard) they will lose 2 life, and then half their remaining life rounded down.
If you control a Brutal Hordechief in your graveyard, when you attack during your turn each creature you attack with both alive and in the graveyard will cause the defending player to lose 1 life and you to gain 1 life. You also may use Hordechief's activated ability during combat, before blockers are declared.