I've never had a problem in MP and I play Oak too.
First, what does your build usually look like? What items do you usually go for?
What I find for Oak is that the early game is very specific to the situation. Many people seem to say he's weak early on. That may be true to a degree, but I think it's more accurate to say he has certain exploitable weaknesses early on and you must play your cards right.
So, you may be finding you just can't seem to control that lane early on. I'm going to talk from a cataract viewpoint here, but this is all generally applicable to everything. What you need first and foremost is...
1. Staying power. You are going to be taking damage if you want that lane+flag, especially against ranged demigods. You need the ability to stay and stay hard. The single biggest thing you can do is get monks from an idol. I, personally, absolutely swear by these. A 10% heal every 8 seconds is massive, and you can pick up a pair of monks for 180 gold if you buy and resell the idol with your starting gold. They do so much I'd pay the 900 for the idol if you couldn't resell. Priests also add a significant chunk of dps and they are ranged. Very powerful.
Scalemail. 400 gold is ridiculously cheap for 600 armor. 600 armour is ~18% further damage reduction. Also, any damage reduction makes your hp regen more effective. Banded armor gives +24% health to your starting health pool. Good for priests' percentage-based heal, plus you get 4 hps. The downside is it's 37.5% more expensive - half a rejuv potion. Budgetting your starting items is always tricky, but definitely get both of these early on because cheap items give more stats per gold spent.
Always have potions. 1 or 2 rejuv potions off the bat helps oak so much. Mana or health potions are not replaced by them, though. Rejuvenation potions are more cost effective for the total hp/mana regained but often you just don't need both. Oak does seem to need both early game, however. (also, if you don't pick up a scaled helm from the start, a mana potion gives 1000 back. Your mana pool doesn't even hit 1000 until a few levels, plus you will have a few hundred mana you can't spend because ability costs are higher.)
The important thing to note about potions is the tipping power of them. That is, 750 hp from a health potion at an important time is much better than 750 hp at a tower before you go back in the fight. That's what makes the cost worth it. It's the difference between him going back to his crystal or not because of a crucial outcome.
2. Doing your job. You've got the staying power to be able to run around trying to do stuff, but what exactly you do highly depends on what you are facing. If it's a melee DG you will have a much easier time hogging the lane. Using your staying power from above, you can often go toe-to-toe with him and send him retreating while your monks fill you up to 100% again for free. In this situation, you might want to go with soul power and a rank of spirit ward after penitence to increase melee damage drastically (+20 from soul power, +20 more from soul power and 1 spirit up activating it, and another +20 from just plainly having 3 spirits active). Unlike many people think, each rank of soul power gives +40 damage. You just need 1 spirit active to gain the second +20. You get a further +20 for every 3 spirits alive. And don't forget to use your 3 spirits! Just don't let them die to towers. When you get shield, divine justice, or others is highly dependent on how you think the early game will play out.
Erebus - he can drive you away sooner with bite. He doesn't have infinite mana, however. If he doesn't have monks it'll be easy: Pull back to your tower (not too late) and let your hp be healed up as you continue to gain xp from waves. Don't waste your mana. Only penitence when you are toe-to-toe and it's a dps race. You have much more staying power than him and much more autoattack damage. If he can't bite anymore then you win and get the lane to yourself. If he bites for ages then he's chugging mana potions and you aren't spending that gold, plus he has worse gear from the start. If he has monks too then prepare for a long tug-of-war over the flag. Just try and keep it as much as you can while you level and get gold. You can also ask for a lane switch or go cap another flag while your monks heal you.
Unclean beast - Funnily, I find this the opposite of the above poster. As far as I have found you will trounce him in melee and send him to his crystal if he engages before level 4. Monks easily keep on top of level 1 spit damage. Try and get rank 1 shield for when he hits level 4, though. Rank 2 spit hurts a lot more and you can cancel it by shielding. If the timing and position is right, you can be cancelling the spit and getting free hits on him at the same time
Sedna - If she's pouncing you, let her waste her mana and just dps her with your superior autoattack. If she picked up heal as well then laugh as she is oom after 2 seconds. If she is just being stubborn and healing, make sure you attack enough creeps so that yours win. If there are 5 minotours and 2 archers and yours are all dead, you're going to be pushed away from the flag with their dps+sedna. You can go, say, penitence > divine justice > shield > penitence against sedna depending on the situation. You have less damage, but you have more hp and mana regen from killing stuff and a shield. This is important because sedna tends to work well with a partner showing up. You're not going to be able to stand toe-to-toe in that situation.
Rook - his towers can seem daunting, but Oak can be underestimated here. Before level 4, rook can only have 2 towers up. You can go in at the right moment and cut a large chunk of his hp bar right off. They key is to attack him in bursts, and at the right times. Interrupt structural transfer with penitence. Try and go in suddenly with an allied DG. That can usually results in a kill. Even if you don't stop him getting a large farm up, you should have blocked a lot of his momentum and kept your xp up.
Against ranged DGs it can be frustrating, but you can do well with the right actions. The problem is the ranged harassment, right? They damage you, you can't get close for payback. Well monks for a start mitigate those potshots they take at you. Now, the important thing here is to keep control of that flag. If he's defending/capping the flag, you can hit him and win if he doesn't run to a tower. If you're defending/capping the flag he can hit you from safety. So as you can probably see, capping the flag is much harder than defending it. So make sure you use your consumables/abilities/whatever to cap it, then you can hopefully maintain the advantage in defending it. It doesn't matter if you're not directly "winning" versus him. If you have the flag you are winning even if you are hiding next to your tower most the time.
Regulus - Annoying range. Get armour to mitigate his autoattack. Don't walk on mines and use disposable minions to clear them if creeps can't or you want them cleared fast. If he's good, don't count on getting near him. Use rank 2 penitence to damage him if you have plenty of mana. Use minions to damage him. Spirits work really well to drive him into tower protection. Priests do nice dps but don't let them die if you sold your idol. I find that archer idols are great. Now, if you find yourself in melee range and you are prepared, then there's a good chance of getting a kill. If you have hp, mana, a potion or two and have enough speed to stay on him, he's dead unless he is also fully prepared with health potions. Look at the hp bar on the right of the screen. That one is actually accurate and shows you the exact numbers. Judge how many hits it will take and how much damage you are taking. If you know he'll drop below 400 as he is dissapearing into a pair of towers, rank 2 penitence and he's dead. It only takes 3 hits to get him from 1k - half his hp - to this mark.
Torchbearer - Banded armour instead of scalemail here. Interrupt his fireballs when it matters, like when you are closing in to drive him away from somewhere. Random fireballs every now and then are easily healed by monks. If he is ice, your monks should keep on top of healing rain of ice easily. You can get a kill in the same way as with regulus.
Wow, that was a lot longer than I thought it would be. Don't forget the basic strategy that applies to every DG. You can't fight 2 DGs, map control, etc.
