A Strength-based rogue can work fine, in principle. We actually have questions about using sneak attack during a rage (Pathfinder-based, but the relevant rules are the same) and seeking prestige classes for a stealthy barbarian/rogue, so the concept is actually one people pursue on their own. As those questions suggest, barbarian is often a decent choice for those concepts.
Specifically barbarian is a strong contender for a single-level multiclass dip: one level gets you rage, or perhaps even better whirling frenzy. That gets you an extra attack, not to mention more HP, more Strength, and so on. It’s also the half-orc favored class, so you don’t take multiclass penalties if your DM enforces that awful rule (almost none do, but then your DM thought this randomized campaign was a good idea so he might also think multiclass penalties are a good idea).
With only one level in barbarian, you only get rage (or whirling frenzy) once per day. More barbarian levels only accrue more rage very slowly, so that isn’t generally worth it. One idea that is kind of interesting is half-orc paragon, which gets a daily use of rage at 2nd level (and +2 Strength at 3rd). Whirling frenzy is explicitly a variant on rage, rather than a barbarian thing, so you can use half-orc paragon rage for more whirling frenzy. If multiclass penalties are in play, racial paragons luckily don’t count towards them, so you needn’t worry yourself about that.
(If you don’t take half-orc paragon, though, you may ultimately resent your race immensely: half-orc is a terrible race that offers you almost nothing useful, certainly not worth its own drawbacks. At least with half-orc paragon, you’d have something nice from your race.)
The other multiclassing to consider is two levels of ranger, since it can get you Two-Weapon Fighting without 15 Dexterity. It could also get you Improved Two-Weapon Fighting but six levels is a lot for what ranger is offering, at least in an SRD environment where other ranger options aren’t available. Eleven levels for Greater Two-Weapon Fighting is just right out. And if multiclass penalties are in play, you’ll suffer as soon as you have more than 3 levels of rogue.
Is this worth it? It may be: rogue is a fairly underwhelming class, and extra attacks make the most of the best class feature you do have. They also reduce the amount of sneak attack you gain, which is a shame. And you could always bite the bullet and have high Dexterity for Two-Weapon Fighting.
I would probably dump Dexterity either way, though, even if you decide not to go with ranger. It would just mean skipping Two-Weapon Fighting, and that’s OK. Whirling frenzy already gives you an extra attack, and Improved Two-Weapon Fighting only comes much later and at a stiff enough penalty that it likely won’t hit anyway. Thus, no matter what, you still want a big two-handed weapon to swing at people, to take advantage of your Strength score. Your source of sneak attack will typically be flanking. But with a two-hander and Power Attack, you are less reliant on sneak attack than most rogues.
The big question to me is whether or not your DM will go for some highly-technical rules-as-written lawyering. Specifically, the rules for double weapons allow them to be used as if they were a paired one-handed weapon and light weapon for attack penalties. Which means that, strictly-speaking, their damage rolls are not treated that way—they are still treated as if the double weapon was a two-handed weapon. This allows a double weapon to benefit from the 1½×Strength to damage and 2-for-1 returns on Power Attack, which is awesome on a high-Strength character who nonetheless has Two-Weapon Fighting. But it’s also quite certainly not the intention of the rules—Wizards even published a prestige class later on that gave that benefit as its capstone feature.
But you also have a rather weak combination that wasn’t your own choice—your DM may give you this one, perhaps. If so, two levels in ranger to get Two-Weapon Fighting while dumping Dexterity, and three levels of half-orc paragon for whirling frenzy and even more Strength, are well worth considering. If not, then ranger probably isn’t worth it; half-orc paragon may still be, but also maybe not.
Anyway, aside from the level of barbarian and the possible levels of ranger and/or half-orc paragon, the remaining levels could be all rogue, or some of them could be assassin. You couldn’t use spells or study for death attack during a rage (though you probably could study someone for three rounds, and then fly into a rage as you perform the death attack), but spells are useful out of combat and death attack is pretty weak anyway. And prestige classes don’t count for multiclass penalties, if that is a concern. Assassin would grant more versatility and HP; rogue would offer more skills and the high-level talents, which are OK-ish.
Another thought worth considering is the horizon walker prestige class. A single level for the desert terrain mastery option nets you immunity to fatigue, including the fatigue that comes after a rage. Not supremely useful (with only one or two rages in a day, you’re unlikely to want to end it early), but fatigue is a nasty enough condition that it may be worth, say, a 3rd level of ranger to get Endurance. And if you stick around for six levels, which is admittedly quite a lot, you can get the shifting planar terrain mastery, which lets you use dimension door once every 1d4 rounds: that’s some decent battlefield mobility not usually available to a character like this.
Some feat suggestions:
- Power Attack is a must-have, assuming you take my advice about a two-handed weapon.
- Exotic Weapon Proficiency (spiked chain) is a particularly good choice for you, assuming you cannot do the double-weapon trick. It allows you to get up in people’s faces and flank them, while still having reach for attacks of opportunity.
- If you are going with a double weapon, I really recommend just using a quarterstaff. The d8s of an orc double-axe are only an average of +1 damage over a quarterstaff’s d6s, and that’s just not worth a feat.
- Stand Still is listed in the psionic section of the SRD, but it’s not a psionic feat or in any way psionic. What it is, is rather good. It allows you to perform some battlefield control. Best with reach, which means you have a hard time combining it with a double weapon.
- Improved Trip is too expensive to take normally, but a second level of barbarian can get it for free, without Combat Expertise or Int 13, if you are a wolf totem barbarian. Worth considering, at least with the spiked chain, as they can trip and then you get a free attack, which is better than Stand Still. Stand Still is still worth having since it works on those you cannot reliably trip.
- Two-Weapon Fighting is available from ranger, but otherwise the Dexterity requirement is, I think, too expensive. Improved and Greater are both very, very expensive.
- Combat Reflexes would prevent completely dumping Dexterity, but even with Dex 12, it would be worth it with Stand Still and/or Improved Trip. Not really necessary, since even one AoO a round is pretty good, but could be useful. Might even consider it after picking up some bracers of dexterity at high levels when they’re quite affordable.
- Hold the Line and Knock-Down are good choices to extend the Improved Trip and/or Combat Reflexes options.