BotS == Blade of the Serpant. It's a favor item that Beast can use to regain mana. Basically, he converts the damage he deals over 10 seconds into mana. Starting with level 2 Spit, he can spit and GAIN mana. Ooze just seals the deal.
Blood == BotF == Blood of the Fallen. +800 HP, +5 hps. Most popular favor item in the game and quite argueably the best for the vast majority of builds and situations.
oom == out of mana
A BotS beast has constant mana which means he can spit recklessly, which is great in team-matches. However, he is at a ~900 HP disadvantage to a Blood Oak AND doesn't have monks. You should be able to dominate his face 1v1.
ShakeNBake just whines about UB don't mind his jokes about him being OP/anti-melee.
Locking flags is ... not the best idea really. 1v1 locks are expensive and even if you lock the gold flag (45 seconds for 4 gps) you are spending 250 gold to guarentee that you get 180 and you enemy doesn't. Hard to justify. Locking flags is huge in 3v3+ games and powerful if done conservatively in 2v2 (lock too frequently and you'll find yourself outequipped).
However, Shield III (arguably Oaks' best ability) lets you use Health Potions, Locks, Teleports, etc with no risk. Shield III is /uninterruptable/ which means Beast can't stop you from potting or porting or locking in his face. He can grasp you, but you'll just lol and walk away.
Shield III and up removes debuffs which means that Spit will be "cleansed". If you are POSITIVE you are going to win a battle, you can shield as soon as Beast spits on you a second time. You'll negate the last few seconds of the prior spit while completely negating his second spit and his dps for 6 seconds. It's pretty nice, but an Oak without a shield is very much "at risk". So be careful about doing that.
A valuable source (if outdated) of information can be found here: demigoddb.com
A slightly uglier but more up-to-date (overall. most of the builds there are crap, don't use them) source of information can be found here: http://demigod.wikia.com/wiki/Demigod_Wiki