For the moment, let's assume you're getting your overdrive from a pedal rather than your amp. If you place the boost before the overdrive, you're pushing the overdrive harder and should get more drive as a result. If you place the boost after the overdrive, you're boosting an already overdriven signal, so you should get more volume boost.
In short, you can use the booster to primarily increase either the drive or the volume.
Since the overdrive is coming from your amp, not a pedal, the de facto placement of your boost pedal is before the overdrive, which will serve to increase drive (or cause the amp to break up sooner, if not already breaking up). This is what guys like Clapton, Iommi and May did with a Rangemaster boost to get more drive.
These days, you can get a clean (FET) boost that will do more to focus on just bumping the volume of the amp. You'll still get an increase in drive, but there's less coloration when compared to a treble boost like the Rangemaster. I don't know much about the MXR or Duncan pedals, but I think the Bad Bob should do the volume boost you want when kicking into a solo. I use a Keeley Time Machine Boost, and one side of it is a clean FET boost capable of doing just what you had asked.
As for pedal order, most will tell you "There is no right way to set up your effects." However, there are places to start with effect order that make logical sense based on minimizing noise and maximizing utility and tonal control. Try this at first:
wah > boost > gate > delay
I'd keep the gate before the delay. Otherwise, you run into the possibility that the gate will clip off some of the delay's repeats if they're subtle enough. However, placing the gate after other effects is nice because it can reduce any noise they produce when you're not playing.
I like to have the wah at or near the beginning of the chain so I'm getting as pure a tone sweep as possible. That would be affected (quite literally) by putting the boost before it, which isn't what I'm after, but this is where the experimentation comes in. That may be just the ticket for you.
Leaving the delay after the wah means that, when both are engaged, the dynamics of the wah sweep are sampled and repeated. If you put the delay ahead of (i.e., before) the way, you have the ability to sweep the repeats. For example, you could pluck a note with the wah in toe-down (treble) position, then sweep the wah back to heel-down (bass) position and get a different tone on the delay's repeat. If you have the delay set for multiple repeats, you can affect all of them with this way, since the delay's repeats are feeding -- and therefore affected by -- the wah.
Mix and match, see what works. You don't have a ridiculous amount of pedals, so it won't take months to exhaust the options and see what works best for your style.
- Keith