Well here's a little bit of a problem. Effective when considered to what, and at what time? The medieval period lasts for about a thousand years and went through a lot of technological and social development to change how people fought.

The simplest answer would probably be that yes they are effective at what they are designed to do. So to break it down, in general there are three major methods of harming an individual with a weapon: blunt force, piercing, and cutting. You can make the case that hacking with an axe is kind of a combination of blunt and cut, but I'm not going to get into that.

Against an unarmored opponent any of these methods can kill. However, how easy it is to kill is another matter. Now each of these methods can kill instantly, but the likelihood varies for how you're using the weapon. A deep cut has a high probability of stopping the fight away, if your arm is cut off your body goes into shock, if you cut open the belly the guts can fall out and there's not much a person can do about that, cut across the skull and even if it isn't fatal, blood gets in the eyes and makes everything much easier. A stab is probably the most likely to kill, but, it takes time to go into effect. You can run a man through and there's a chance they'll still be up and fighting until they fall over dead or bleed out. The weaponmaster George Silver touched on this with why he disliked using the rapier. Then comes blunt weapons, in general these had the least chance of stopping a fight or killing outright. They still could! Smacking someone full force with a mace on the top of their head will kill them instantly. But a person can keep fighting with a broken arm or broken rib, and since medieval medicine was at least decent at patching bones even a broken skull was not necessarily fatal.

There also comes the problem of reach and weight. So a lot of people seem to think that medieval weapons were unusually heavy, and that bludgeoning weapons are the heaviest of the lot. This is not necessarily true. Perfectly honest, a good one-handed melee weapon ranges from 1-3 lbs. That can be 1-3 lbs of sword, 1-3 lbs of mace, 1-3 of axe, it doesn't really matter. You want to be able to keep swinging this weapon as long as you need, you do not want it to be much heavier than that, ever. So if you have 1-3 lbs to make your weapon, if you're making a cutting weapon you can spread the metal out over a long length rarely getting the weapon particularly thick. So the weight is pretty evenly distributed so the point of balance is somewhere along the blade fairly close the hands, this allows the weapon to be both long and maneuverable. If you're making a piercing weapon, you can go even longer because you don't even need the blade to be particularly thick or wide, so long as it ends at a point. So you can put the weight even further back towards the hand allowing even more maneuverability. Now for a bludgeoning weapon, the head needs to be thicker and heavier than a comparable cutting or thrusting weapon. This means the weight of the weapon will be distributed further up the weapon, making it harder to maneuver. This will make the weapon feel sluggish if you're used to a sword.

So facing an unarmored opponent, honestly, blunt weapons will still work, but probably aren't the best tool for the job.

And so for a good portion of the early medieval period where armor was scarce we see more of a focus on spears, knives, swords, and the occasional axe. This is a gross oversimplification. Maces still existed and were used, but looking at weapons found in burials they seem to be not favored by those with the wealth to afford other weaponry.

But as time went on, armor stated to become a more common feature on the battlefield. There were padding armors of layered cloth, which was very effective. But given time could still be torn and run through so other weapons are still your primary focus there.

But during the Viking Age we see descriptions of the most elite warriors in their respective culture covered head to toe in mail. Now, chain links of mail is very good armor, the Romans used it for most of their time of conquest. It remained an important part of armor almost until the end of armor's effectiveness on the battlefield well after the medieval period ended.