Those undead vampires might be stronger and faster, but a sword would give more reach, and could lop off a limb. I very much doubt the monsters fight better missing an arm or a leg?
Silver may be useful as a 'magical' metal, but it's a pretty soft metal otherwise. A silver sword would go blunt & get bent/crumpled pretty quickly in combat. Plus, a stake is easier to carry and conceal than carrying a sword; particularly when in public places. Besides; decapitation doesn't require silver, just something capable of doing the job.
Fire can be used to fight Strigoi; but unless you're carrying around a flame thrower, or white phosphorous grenades, it won't kill them quick enough to stop them. They could be blown up or incinerated, but you'd have to get them to hold still for that. Since they rarely get advanced warning, melee weapons work best.
"I enjoy the sight of humans on their knees. That was a joke." EDI
"Plus, a stake is easier to carry and conceal than carrying a sword; particularly when in public places. Besides; decapitation doesn't require silver, just something capable of doing the job."
The stake put you in close quarters were the enemy excels. No wonder it takes 5 of the best guardians to kill 1 bad guy.
The strigoi don't attack at range, so it'd be unusual for Guardians to see them coming from a distance, if say, they were using heavy duty ranged weapons. Don't get me wrong, I'm sure a .50cal would be extremely effective against them, but in the movie, don't a bunch of them just drop in, appearing only a few feet from them at the start of the movie? I'm sure in the books, they also carry guns, but they are only partially effective I suppose.
I'd guess it takes five guardians because they are only around as strong as a human, whereas the strigoi are, well, 'vampire' strong.
A group of guys all carrying cane swords would look a little bit conspicuous I think. It might interfere with the bodyguarding too, if they had to make it look like they needed a walking stick.
"I enjoy the sight of humans on their knees. That was a joke." EDI
When I said close quarters, I meant it as in hand to hand. A sword or similar size weapon gives you reach that keeps you just outside of that zone.
We see strigoi twice. The group drops out of tree and Natalie sneaks up and kills all the guards. They seem to like stealth. Also, they're cocky. At least Natalie was very cocky.
As for the conspicuous angle, the strigoi don't attack in large public gatherings of humans. They must have some vested interest in keeping thier existence a secret as well.
Actually we see them 3x...Lissa's dream/nightmare as well. I understand your thoughts on the sword,I thought it myself while reading the book, and it would have worked for the movie with the....cheesy....changes and distances it added.
Also, on fire,I believe this is where the Moroi would be handing in the fighting with the Dhampirs. Look at how well Christian took care of the sci-hounds. ;)
It's not mentioned in the movie I don't think but the summer must be blessed with the magic if the 4 elements by a moroi.