I thinking of doing a katana wielding character. I usually take low strength so I'm curious how much strength plays a role if at all.

http://fallout.wikia.com/wiki/Melee#Fallout:_New_Vegas

For the Katana, I'd say above all it's important to have high Luck and to NOT take Heavy Handed.

Generally Heavy Handed is superior to not having it, but a couple weapons are an exception. The Katana is one of them.

Agree with this. I'm currently running a stealth melee/unarmed assassin, and the Katana is one of my key weapons (also Gehenna). Its got a very fast attack rate, especially with perks and weapon mods) and a higher than average critical chance. Strength is not important with this weapon, and taking Heavy Handed is counter productive. Have high Luck, Built to Destroy and the usual melee/unarmed based perks.

Sounds like fun. I'll counter it with a .45 silenced and placed satchel charges/c-4.

Strength is only important to meet weapon/perk requirements. It has a neglible effect on damange, so get the bare minimum necessary for your build (unless you like the extra carrying capacity).

It effects the base starting point of your Melee skill (amoung others) it is worth have to avoid pump more points into it.
A STR of 8 is the best to take as it allows the use of all weapons with ease
Also if you don't meet the requirement the weapon is weaker iirc

Problem with high strength is it comes with the ability to carry ridiculous amounts of gear. I never go higher than 4 and sometimes 2.