How are club-style weapons effective? The First Law of Thermodynamics states that I can't swing an object held in one hand with more energy than I can swing my arm, and the Second Law says that the total energy would probably even end up being somewhat less.  And yet, a person who might not be afraid of getting punched by me would certainly be more cautious if I had some sort of blunt object, such as a club, baseball bat, or crowbar.
If it were a blade, I could understand that: the edge focuses the impact down to a much more concentrated line.  But a blunt weapon doesn't do that, so how is it able to be an effective weapon, hitting harder than you can hit with an unarmed blow?
 A: There are several reasons:


*

*It is hard. That's why even wearing a knuckle duster will increase the damage you do greatly. And wearing boxing gloves decrease the damage you do.

*Humans are more strong than they are fast. I'm a bit oversimplifying, but the limiting factor in giving a strong blow is not the energy or force you can exert, but rather how fast your hand can move. You can have the same blow speed with a brick in your hand, but again, cause much more damage.

*It is long. This is again related to the second point, by using a longer object and more force, you can have an even faster moving point of contact and momentum\energy, without having to carry a very heavy object around.

A: Three answers have not yet been provided to you; I'm afraid that the true answer is basically "well, for lots of reasons."
First, you have not understood a reciprocity effect yet, which is that when you punch someone with a fist really hard, it hurts you. So that tends to be a natural limiter in fist-fights that is not necessarily there with a weapon: there are plenty of movie scenes where someone "snaps" and attacks with a weapon and keeps beating and beating them, not totally conscious of what they're doing. It's harder to get into that state when every punch potentially dislocates a knuckle or inserts miniature cracks into your phalanges or twists your wrist the wrong way.
Second, there is a reach effect; if someone else is armed and you are not they can have an added benefit of distance.
But let's talk about the third, and that's "how does material failure happen in the first place?"
Materials usually deform and break due to a stress, which is defined as a force divided by the cross-sectional area that it acts upon. Different objects break with different stresses along different axes, so unlike pressure it's not just one "force/area" number which is constant in all directions at all points, but nevertheless that's the correct way to think about breakage.
So you've already indicated that you understand the "area" effect, which is that a blade does a lot more damage than a club simply because the cross-section is a lot smaller, and that bulletproof armor protects us because it makes the cross-section of a bullet a hell of a lot larger. However I would also say that the cross-section of a club can be much smaller than an arm or fist. Notice that the curve of these objects means that some relatively small surface hits you first, and it only later expands to a larger surface as more of that curve touches you. So there is some effect here, it's just not so pronounced.
But the "force" effect is far larger, and this takes a bit more understanding.
Newton's laws say $F = \frac{dp}{dt}$ and therefore $\Delta p = \int dt~F.$ This means that a momentum change is a continuous sum over time of a force. The momentum of your bat is the sum of a bunch of force you put into it over a second or two. Then what? Well, it's very hard and rigid and it stops in maybe a tenth of a second or so. This means that these "time to swing" factors are really "force multipliers." The softness of the object also creates a "time to impact" which is naturally going to be longer for your many-moving-parts fists than for a rigid metal object.
This is basically just the concept of leverage restated. You sometimes see people at the beach walking their dogs with these "ball-thrower" sticks. It becomes effortless to play very long (in the sense of distance) games of fetch with your dog, using this stupid little stick! How do those sticks work? Well, following the above description: they give you more time to push on the ball. Equivalently, we might say they form a lever system with your arm, giving you a mechanical advantage. These two ideas are fundamentally the same idea in the underlying physics. When you swing a sledgehammer, because it is massive, it moves slowly, and you get a lot of extra time to push on it. The mass acts basically like a form of dynamic "inertial leverage," letting you store up more force as momentum to create a greater impact force. It's the same as if you've got a bolt that you can't get unstuck even with your wrench, so you grab a heavy hammer and bang it hard against the wrench in the direction you were pushing: that's a form of this "inertial leverage" too.
In fact if you think about it, there are some other force multipliers, too. Have you seen a child pitch a ball, versus a grown adult? The child does most of the throwing with a quick snap of the arm and wrist; the adult throws by winding up for an extended time with their whole body, you see them get their back in on the action as well, and in some ways really professional pitchers in baseball etc. remind me of something like cracking a whip.
I've seen people "follow through" on their punches before, and that's where that idea comes from; you get more muscles in on performing the punch. However it's quite possible that people simply naturally swing a lead pipe with more muscles than they would their fists. This is a second effect that would increase the force and hence break more stuff.
A: The answer: It's less soft. 
It is not as important how much energy is transferred, as how fast. Something more soft makes the impact last longer. The soft material dissipates some energy during its deformation. 
You can see this from the momentum version of Newton's 2nd law:
$$\sum F=\frac{dp}{dt}$$
You need to make a certain change in momentum $dp$. If you can do that very faster (small $dt$), the force is huge. 
A: I think one of the reasons is a club is much more rigid (has a much higher modulus of elasticity) than a hand. @Countto10 mentioned the lever effect in a comment, and that may be important, but rigidity is important as well: a knuckle duster is much more convincing than a bare hand, although it does not use the lever effect. 
A: As George Carlin said, "It's amazing what you can accomplish with a simple baseball bat."
It is mechanical advantage. Work is force through a displacement $W~=~\vec F\cdot\vec x$ For the force and displacement parallel and $F~=~ma$ and $x~=~\frac{1}{2}at^2$ it is not hard to derive with $v~=~at$ that
$$
W~=~K~=~\frac{1}{2}mv^2,
$$
which is kinetic energy. I leave that as an "exercise" to show this. So suppose two extended objects of lengths $\ell$ and $\ell'$ are moved with the same energy. This means that ratio of lengths is equal to the reciprocal forces. This is how a lever works. So for $\ell~<~\ell'$ we have $F'~<~F$. This sounds bad, but for an extended object the ratio of the lengths means the end of the more extended object has a larger velocity. 
