For cold, nothing beats chillheart weapon and either nightblade or inquisitor secondary afaik.
For lightning, yes shaman has nice support for lightning and 2h, but the best endgame set for lightning EoR is the cyclone set, which forces you into 1h+offhand. It got nerfed multiple times, however the lightning EoR part actually got a small buff this patch. It should still be good.
About yugol’s relic, yes standalone it’s weaker than EoR. All abilities from relics/sets/components are generally a bit weaker than a fully specd mastery ability. They are mostly meant to be filler abilities. So for yugol you’ll need the support of dot or nuke abilities.
For EoR Oppressor(+necro) physical, aether or vitality damage should fit the class best imo.
The best 2h EoR playstyles I know of are chaos Sentinel with tenebris scythe or possibly vitality Sentinel/Oppressor with some vit scythe (don’t remember the name).
To get a general overview over the items that support EoR go to grimtools.com click on item database and search for eye of reckoning.