IMO erebus is almost as good against reg too... I use cloak tp+bite followed by a chase if I smell blood and it's good times.

I think erebus+ub is just a very good combination in general.  Both pretty competent 1vs1 at holding lanes, and with the chain stuns (foul grasp + sleep, then bite for slow) an extra cm at the wrong time could very quickly become an overextension.

Sorry, I don't have much constructive advise on beating the combination though.   Perhaps the biggest thing is to "hold out" until end game.  This is where oak and reg become very powerful.  Yes, mines are a very powerful counter particularly for melee demigods. One thing you do have going for you is that the other team might be afraid to tech their creeps (because surge of faith + souls is so good for oak); you'll probably be behind in war rank most of the game, but if the opponents sit on their war rank too long a quick tech would put the hurt on (on the other hand, yours is probably a more expensive combination anyway so you'll probably need money for gear... hmmmm).

I'd say you're wrong right here at first. Cause banded mail does give you a 600 HP buffer, but priests will heal you for far more over a combat. Try to get priests + 1 combat potion, and in 1v1 i almost garantee a kill vs beast (in early game ofc). Ereb can be tricky since he can have priests too.

Erebus is very hard to kill because he can run away/mist so in general I would focus fire on the UB unless I know Erebus is low on mana. Another idea is to wait till he goes into mist and throw mines where he will be when he gets out of mist form. This is very LOL.

Erebus/UB combo is pretty tough, especially when Erebus' minions can kill you on their own. 

I don't know oak that well, but i play regulus a lot. I stack run speed, and hit and run. Erebus is extremely difficult as he is fast and teleports. best strategy I have against erebus is to throw 6 mines at my own feet and stand on them as I peck at enemy towers. force the fight to me and then run. He'll take a lot of damage when he reaches me and won't give much of a chase. I'll stack 6 more mines and poke at towers some more. I'll try to inch my way into their base. I start regulus with speed anklets, banded mail and a healing pot + sight radius and a flag lock. Then I work towards getting the 550 mana helm and boots of speed then unbreakable boots and eventually vlemish and slow proc gauntlets. Afterwards I just spend everythingon consumables and boosting the citadel. With priests not feeding, dropping 1800 is a pretty good bargain. Those 2 don't exactly have excellent AOE, definitely compared to surge + mines. If you have a bigger army on your side can often tip the tides. Having max range and hiding behind waves of creep is a good idea.

Try to win the war score game.

Minions move slower than erebus. If you're going to take the time to do that I will have plenty of time to run. Erebus is deadlier if he catches you offguard with his swarm.

for Oak,

starting items:

Blood of the Fallen (favor)

Idol Priests

then buy Banded Armor and Scaled Helm as your next two items, you'll get cash for that very quickly.  within the first 5 minutes or sooner. 

you'll need at least rank 1 Shield to escape the pain train when they decide to focus fire someone. wait to Shield until after they've used Spit and Bite though so you can clear the debuffs. despite the tooltip, even rank 1 Shield will remove all debuffs on its target.