All my advice is based on NA prices; I don't know how much EU prices differ.
A 30% elite damage SoJ would add enormously to your dps where it counts, and even a cold damage 30% SoJ could be had for much less than you 100m budget. I recommend not worrying about getting one with a barbarian skill; it drives the price way up even if the skill bonus is something utterly useless.
You could also quite easily obtain more strength from your IK helm and belt.
I recommend moving away from the BK swords. They look really cool and give tons of strength, but being stuck with a set is restrictive and if you aren't going to use Weapon Mastery for the chance to proc 3 fury per hit with a Mighty Weapon, you might as well be using a high damage-per-hit mace or spear in your main hand and something fast (or Echoing fury for the +.25 aps to both sides) in your off hand. You're also in the damage range where life steal becomes more powerful than life on hit (except vs health link/health link+reflect damage) so you might keep that in mind, too. But changing weapons is a big endeavor and gives you a lot to think about; it is difficult to recommend anything too specific.
I thought of the stone of jordan, but I don't really like it (probably because no strength/crit/atk speed, which is a bad reason, I know). Could someone playing with a SoJ post a feedback about it? Like the real improvement to the dps on a boss fight like Asmodan?
For the weapons, I totally agree with you, I just bought BK's swords because at the time, for 200M, you had a great pair of those, and it is good. I was thinking in saving money for an echoing fury (strength, socket and crit dmg) and a 300th spear to switch on a throing build, but even if I could save up to 200M or 250M, 500M seems a lot to me and I am looking for advices to improve my gear for a lower cost. The thing with BK's swords is that you have lots of useful thing on it, which makes it hard to replace, as you pointed out...
I have and use a 30% elite damage SoJ with cold damage. It is the best single upgrade for actual dps per gold spent I've ever made. I think it cost me 12 million to have all enemies that get hit by my whirlwind or tornados slowed, plus 5% extra dps against them (all 'black' damage on both of my weapons) that pretty much covers the dps my previous ring was adding, and then vs elites... well, not much compares to a 30% increase in damage.
The calculator I use for whirlwind/sprint dps indicates that even a 200 strength, 9% attack speed, 6% crit chance, 50% crit damage ring doesn't give me the same dps vs elites that my cheap SoJ (with non-perfect cold damage and a bonus to a wizard skill) does.
Karth is correct, with all he said about the cold soj.
The issue is that the character sheet dps will not show the 30% boost against elites. It is huge, it helped me farm mp6 and 7 much more efficiently. It is also a big reason why my brother and I are able to farm ubers on MP7.
I have a ring that has 28min-45max damage, 77str, 8as, 4.5crit hit that adds life 15k dps over the soj. But using http://www.d3rawr.com/ the soj actually gives me 30+k more dps to elites cause im right around 100k dps unbuffed.