It also needs to be known if the settings for the match were 'High Gold'.
If that were the case it would be feesible for Oak to atleast obtain slayers and gauntlets of brutality on his own, or, have one teamate buy those and feed him some health items while he saved for Mageslayer.
It's worth noting that DemigodDB doesn't update damage statistic for either Soul Power or Sprits. So you have to add that to the value you come up with independently, right? Doing that you can get him almost to 380ish with just a couple items.
Assuming nothing you've said is exagerated, they wouldve had to feed him items. You just can't do it on a 17xxx budget without it being fed, and taking into account that the budget was only so big after he killed you so much. I have a hard time believing that was the budget if you killed you so easilyl, and seeing as how the game lasted 23 mins. Even on normal maps thats what, 4 gold a second for 23 mins = 5520 gold. Soldiers give 4, and archers give 8 apiece, and he would've had to have been on a lane for that extra gold, which is around what 36 gold every 20 or 30 seconds? But then you gotta subtract the gold generated from level 5+, as that income doesn't count towards the point were trying to get at.
Basically, you paint a pretty hard picture. The only item that would allow him to do that has already been called out by others as Bracelt of Rage, under its +300 affect. Which would pretty much get him there with just soul power and minions. He easily meets 500ish for those 10 seconds. The only way for him to have got that, or any other configuration, is for them to have given him items to sell back off for it. Even with magical coin purse, thats still, 12600 gold. Divided by 3 its 4200. Which, considering creeps and regular gold intake, is feasible. It's more than feasible if you had it on high gold income, or lost any towers, or had a death early on that you can't seem to recall.
I can come up with other configurations that get 380-450, but can't have a feasible gold condition, or leaveing any slots open for Health Items.
If you were even the slightest bit uncertain about some of your memory, it would give many more options to consider. But from the sounds of it, he killed you a lot...so he couldve easily thrown in 2-3 health items and upgraded to high priests after those first couple kills, and perhaps you didnt really pay attention to his health the first encounter since the face rape was so unexpected.
Thats the most logical answer I can come up with, and the only thing that seems possible given your story.