As a refresher, your primary goal as a supervillain in a social situation is to control your audience and keep them from being too much of an obstruction to your real plans. Very few people achieve their real objective by just standing around talking, unless you count Congress. So let's look at what monologues, dialogues, and verbal wit can do for you.
Control of information
Sun Tzu says, "all warfare is based on deception". Deception is the dissemination of falsehoods or half-truths. Or to put it another way, deception is the control of information. How does your opponent get information? By watching you, but also by listening to you.
What do you want to deceive your opponent about?
The nature of your plan. The easiest way to do this is not to tell him. The more cunning and subtle villain will explain the wrong plan. The cleverest villain will explain the plan and lie in such a way that the hero tries to stop the wrong thing from happening - or actively aids the villain. Not saying anything requires no special skill, so we'll focus on misdirection.
"Die Hard" is the canonical example of this approach. Hans Gruber needs access to a vault that's sealed with an electromagnetic lock, so he tricks the FBI into shutting off the power by telling them that he's got hostages and wants prisoners released. His brother performs a similar act of misdirection in "Die Hard With a Vengeance". The "Mission Impossible" and "Bourne" movies offer similar tricks, but from the hero's perspective.
The easiest way to get good at this is also the most time-consuming: actually plan out all the details of two capers. The first is the one you want your enemy to think you're doing. The second is the one you're actually doing. At every point, think of what you're doing, what could go wrong, and so forth. Then for the fake caper, write some dialogue between yourself and a hypothetical hero, or the police, or whoever you expect to be there. Set it aside, think about something else for a day or two, then come back and re-read all your dialogue. Does it still hold up? Does it give anything away? Can you improve it? Repeat until satisfied.
The purpose of this planning is to come up with specifics. People will be convinced of just about any kind of bullshit if you sound like you know what you're talking about, and the way you do that is to provide specifics. For example, it's common for newbie supervillains demanding money to ask for it in "non-sequential bills". This is obviously a correct thing to ask for, and it gives the appearance of competence and experience doing heists. It won't save you if you actually don't know all the other ways money can be tracked, but if your goal is to sound convincing, it's good.
Your next move. The feint is a traditional tactic. The verbal feint is just a variation on this theme. Your best ally here is expectation - what the hero, the cops, and the crowd think you're about to do. This depends as much on your reputation as your actual caper - a violent villain will be expected to make violent moves. Play up expectations with appropriate dialogue, then do the unexpected.
How well you're doing at carrying out your plan. Your ability to project overconfidence, underconfidence, or confidence in the wrong thing is crucial here. Your ability to emote - to act happy, sad, frustrated, fearful, or whatever - is more important than word choice, so this requires a lot of practice.
Tools for deception
Hamminess. If you saw "Star Trek" and remember Captain Kirk, you have seen ham in action. Same with the 1980 "Flash Gordon", with Brian Blessed as Vultan the hawkman. Ham is overblown, ham is spectacle, ham is panache.
Ham is the tool of choice for two types of villain. The first is the newbie. Someone who's starting out and can't emote deceptively can use ham to mask that weakness for awhile, because the loud bombast is distracting and that's good enough. The second is the experienced villain who's naturally hammy. If ham is in your blood and you've been at the game for awhile, you can get away with it. Most villains abandon ham after they get some capers under their belt, but a few come back to it.
Puns, quips, and word play. Intentionally bad verbal tricks are used to defuse tense situations, lower stress levels, and impart a theatrical air to an otherwise-scary caper. Being able to rattle off funny quips on the fly is definitely a skill that requires more time than I have to teach. As with a lot of things, the key is to practice and keep working.
Like a good caper, a good quip must be used sparingly and not repeated when possible. George Carlin threw away his material and wrote fresh acts every year. He said there's three levels of comedy: funny, funny with good ideas, and funny with good ideas and compelling language. For villains, "good ideas" really means "things I want to make people believe", but otherwise the rules of comedy are a good start when writing such things.
Threats. This is the opposite of verbal humor. Where the intent of corny dialogue is to lower stress levels, a good threat is meant to raise it, or to convey a feeling of menace even when you don't really intend to hurt anyone. This is the tool the veteran villain uses to keep cops at bay, or make the hero question his own actions.
The problem of threats is that they have to be followed through once in awhile or they lose their power. Threats of violence, especially, can lose potency once you become any sort of known quantity to law enforcement, unless you actually do hurt people. Threats against property are far more lasting, and far less problematic to carry out.