Well I've played as a Serious PUP since it came out with ToAU. I can say that Overdrive does not work the way BGwiki stated. It doesn't triple the maneuvers present. You can test that with Auto-repair kits and Light maneuvers.
It does offer Immunity to status effects for the duration. I've seen it resist petrify/stun/sleep/slow/weight/poison/blind/paralyze. Also, if your Automaton is already afflicted with a status effect then Overdrive will work like Benediction and cure all status effects present when activated. (Minus the full health from actual Benediction)
I think what does happen with your Automaton's Attack and Defense is change or remove level correction formulas so that your Automaton will deal maximum damage to targets of higher level(or defense) to a certain degree. Think Ranger's "Flashy Shot" but for all attacks. If your Automaton is already higher level or doing max damage with max melee skill and Tension springs then you won't see an increase.
The increase to defense is hard to gauge, but I've seen slight drops in the amount of damage taken during Overdrive.
The Haste effect is real. However, it does not create a reduction in delay equal to Hundred Fists. More like delay is reduced by ±25% (The times I've tried to see how fast my Automaton can swing I had been equipped with Anwig+5% Pantin dastanas+2 +4% Moepapa Stone +5%, at which time my Auto swings about twice as fast, with turbo charger attached) I hate to say it, but there might be a limit to the max delay reduced for an Automaton. If equipment + 3wind maneuver turbo charger + Overdrive doesn't get my Automaton to spaz out then ~Balls~ to you SE. :(
If I use Overdrive for DD, I make sure I'm using the right maneuvers to get the strongest Weaponskills: Armor Shatterer and String Shredder.