That's a good question, i'm sure you will be getting plenty of responses. (I'm also assuming you mean soul power as opposed to soul frenzy. Please note that it is only worth getting Soul Power I)
Anyways, up to and at level 10 you have 3 choices to choose from. Burst* damage, DPS damage and HP Stacking. I think everyone is in agreement that HP stacking (ie shield) tends to be more effective than DPS stacking. Levels 10-15 you can select another "choice" most games end before hitting 15 as i'm sure you are aware of.
*note burst damage for the oak is not typical burst damage but is essentially leveling up pen and sof to supplement autoattack damage
First off read this thread for a nice heated discussion:
http://forums.demigodthegame.com/366608
For my typical build I like to get Shield I, Pen I and Divine justice in the first 3 levels. I wait to make my selections until I need to. Shield I at level 1 when in doubt. (And never ever post anything different than that on the forums 
For games with higher experienced players on the other side i usually get shield at 1 and pen at 3 however sometimes i try to wait to get shield if possible. My Favorite build doesn't use shield until late levels and is Pen, SoF & Spirits based but i dont get to use that one too much since it is DPS focused.
So in answer to your question. At levels 1, 2 & 3 a minion oak with monks and BoF will be able to push you off of a flag (assuming you have monks & BoF as well). I find that competing with the sustained DPS to be challenging at that time. I find that at level 4 pen II & shield will help push a minion oak off the flag. However the tide really turns at level 5 and up where SoF takes out a lot of spirits and armor mitigates their damage. From levels 5-10 a minion oak poses little threat to the "assassin" oak. At level 14 (reserving 15 for SoF) I typically have either spirits IV or (shield III & spirits II) depending on what's needed throughout the game. My preference is spirits if possible.
Numbers in parentheses are for total spirits at that level
A single spirit at level I does 13 DPS (39 dps), with SoF I enabled it does 14.3 dps each (42.9) , SOF II it does 14.95 (44.85)
Spirit level II does 15.6 DPS (78) with SOF I enabled it does 17.16 (85.8) SOF II it does 17.94 (89.7)
Spirit Level III it does 18.20 DPS (127.4) with SOF I enabled it does 20.02 (140.14). SOF II it does 20.93 (146.51)
Spirit Level IV it does 20.8 DPS (208) with SOF I enabled it does 22.88, (228.8) SOF II it does 23.92 (239.2) and SOF III it does 24.96 (249.6)
To sum up everything my opinion is that Yes the Oak needs spirits at some point. The question is do you go for an assassin build at the beginning or a minion build at the befinning.
Another fun build (for shitz and giggles) is shield at level I and then full spirits + morale with either Ring of Divine Might or Horn of battle as your favor item.
j