More strength = more dps, but how much more?
 

I need someone good at math and knows the damage formula. Assuming person a has 100 str and person b has 200 str, assuming everything else is equal, what percentage more damage will person b do over person a?

between 10 and 50%

It depends on a lot of things.

-100 more strength will let you hit for more damage (higher 'max hit' from strength bonus)
-100 more strength will give you more attack and let you hit for a higher average DI (regardless of what the relative 'max damage' hit is)

On a low level blue or light blue (green) con where you're already hitting for a higher average DI (damage interval - ie more max hits more often) the 100 strength will not have the same impact as fighting higher con mobs closer to your level (or higher than you) in terms of your average DI. Mobs level and ac vs your level and attack will have a big impact on how hard you hit on the DI spread (1-20). For trivial mobs where you hit at or near max more often, the strength won't be AS important, but it'll still make you hit harder.

TLDR cliff notes:

-the difference between 200 strength and 100 strength at any given level will be pretty big.
-if you're a melee class tasked with dealing damage, you should make sure your strength is as high as possible.
-as you get way up there in levels, be aware that you can't go past 255 strength and high level strength buffs may or may not put you beyond the strength cap.

Is Strength one of those stats that gives diminished returns after 200?

yes

Except for how much loot you can carry.

naah after 200 it's decided by loot council

The P1999 wiki has a page on the game mechanics. It doesn't talk about how once's attack rating impacts to hit and average damage of hits, but it does talk about the impact of strength and weapon skill on max damage. This is very relevant before lvl30 and generally only relevant past lvl15. The basic formula is:
(weaponskill+strength-75) / 100

The outcome is multiplied by your weapon damage. The outcome is a minimum of 2 so if you're under a 200 outcome, it is 2 regardless. This determines the damage cap.

So say you're a level 15 warrior. Your weapon skill is 75 (15*5). If you have 200 STR, you'd exactly hit the x2 mod. But once you level up and acquire more weapon skill, you'll be raising your damage cap! This is easiest to achieve for ogres, who with some relatively cheap STR gear and a level appropriate buff, will hit 200 str.

tl;dr: STR helps, acquire level appropriate weapons (max 14 dmg for 10-19, max 30 for 20-29) and swing like a boss.

This much more important than most people think. If you get encumbered you loose AGI and get hit much more and for harder.

My rogue is currently running around with 1700 gold as I haven't been to the bank forever,

However in terms of str I keep mine about 190, as shaman buffs max me out - very rarely will I be grouped without a Shaman around.