Are there any small sized creatures with a bonus to their strength score?
Ideally, I'd like one/some with as close an ECL to zero as possible.
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I’ve found three:
Earth Mephling, Planar Handbook, +2 Str, Cha, −2 Dex, Int. Humanoid (Extraplanar). Gains a Burrow speed, a Breath Attack, a +1 Caster Level bonus on [Earth] spells. LA +1.
Marrulurk, Sandstorm, +2 Str, +6 Dex, +4 Con, +6 Wis, +4 Cha. Yes, that is +22 in ability score bonuses, and yes, that is insane. They also get tons of other stuff, like 2d6 Sneak Attack and a Cha-based Death Attack, Point-blank Shot and Rapid Shot as bonus feats, +2 Natural Armor, lots of skill bonuses (Hide, Move Silently, Listen), Poison Use. 3 Monstrous Humanoid RHD and LA +1. Relatively high ECL but boy, is it worth it for the right build.
Windrazor, Monster Manual II, +2 Str, +4 Dex, +2 Wis, −2 Int, −4 Cha. Main draw is the Fly 40’ (good), though they do have two Claws and a Bite, Improved Critical for both of those, and can scare people with crits. 2 Outsider RHD and LA +2. Not really worth it at ECL 4.
Aside from those, you can take any Small race and apply a Template to it for bonuses to Str. Of course, Templates usually involve LA, which almost always isn’t worth it. Still, for completeness’s sake...
Basically, LA +1 templates that are actually close to being worth an LA +1, and grant Strength.
Draconic, Races of the Dragon, +2 Str, LA +1. Definitely the best way to make a random race “dragonish.” Well, other than taking levels in Dragonfire Adept, or taking a Dragonblood variant of the race, if one exists...
Feral, Savage Species, +4 Str, LA +1. Quite possibly the best template out there... depending on how you read Savage Species’s ambiguous rules. If it scales with any HD (including Class Levels), rather than merely RHD, it’s amazing, quite possibly better than LA +1. If not... it’s OK-ish? Great if you’ve actually got RHD, I suppose, they pull some double-duty... The main draw (Pounce) requires 4 HD.
Mineral Warrior, Underdark, +2 Str, LA +1. Actually quite good. Many consider it too good.
Lolth-touched, Monster Manual IV, +6 Str, LA +1. If it weren’t for the fact that this involves having Lolth touch you, this would be excellent. Again, probably better than LA +1.
That have a Strength bonus, can be legally applied to a Small PC, and leave that PC Small.
These are... pretty much garbage, as far as I can tell at a glance. LA +3 or greater is something I personally won’t even consider allowing in my games (barring Unearthed Arcana’s Gestalt variant, though even then...). To the best of my knowledge, none are really worth it, and even if some were, the sheer skewing that they’d do to your stats (ability scores too good, HD, HP, and Saves too weak) is just bad for a game. Still, they’re here.
Half-earth Elemental, Manual of the Planes 3.5 update, +4 Str, LA +3.
Half-water Elemental, Manual of the Planes 3.5 update, +2 Str, LA +3.
Alu-demon, Dragon vol. 355, +2 Str, LA +4.
Half-celestial, Monster Manual, +4 Str, LA +4.
Half-fiend, Monster Manual, +4 Str, LA +4.
Half-Janni, Sandstorm, +2 Str, LA +3.
Lemorian, Dungeon vol. 143 or vol. 146, +4 Str, LA +4.
Half-dragon, Monster Manual, +8 Str, LA +3. Most Str/LA, but really not worth it without being Large for the wings. (not really worth it anyway)
Half-scrag, Fiend Folio, +6 Str, LA +4.
Half-troll, Fiend Folio, +6 Str, LA +4.
Gheden, Dragon vol. 313, +4 Str, LA +1. Looks good from this synopsis, but has Dex/Con/Int −2, Cha −4, and a bunch of Undead vulnerabilities without actually being Undead. Still, LA +1’s workable; it does get some of those Undead immunities.
Ghul, Dragon vol. 313, +2 Str, LA +3.
Half-vampire, Libris Mortis, +2 Str, LA +2.
Katane, Dragon vol. 313, +2 Str, LA +4.
Earth Elemental Creature, Manual of the Planes 3.5 update, +2 Str, LA +4.
Magma Elemental Creature, Manual of the Planes 3.5 update, +2 Str, LA +5.
Corrupted, Dragon vol. 350, +4 Str, LA +5.
Stoneboned, Dragon vol. 350, +4 Str, LA +2. Gains Powerful Build but you can stay Small.
Mummified, Libris Mortis, +8 Str, LA +4.
Animus, Dragon vol. 339, +4 Str, LA +4.
Gravetouched Ghoul, Libris Mortis, +2 Str, LA +2.
Vampire, Monster Manual or SRD, +6 Str, LA +8.
Savage Vampire, Dragon vol. 348, +6 Str, LA +6.
Shadow Vampire, Dragon vol. 348, +4 Str, LA +10.
Dry Lich, Sandstorm, +2 Str, LA +5 (waived if gained through Walker in the Waste prestige class)
Drowned One, Dragon vol. 106, +6 Str, LA +3.
Fleshvigor, Dragon vol. 315, +2 Str, LA +1 (must already be Undead).
Voidmind, Monster Manual III, +4 Str, LA +1 (but really unplayable, since a Mind Flayer can dominate you at any distance, no save).
Dustform, Sandstorm, +4 Str, LA +2. Loses all base creature’s special qualities.
Hooded Pupil, Libris Mortis, +2 Str, LA +4.
Spellwarped, Monster Manual III, +4 Str, LA +3.
Many thanks to Chet Erez, whose amazing indices make such thorough answers possible. Note that I have not personally checked most of the Templates in the last part of the answer; Chet’s indices have had some minor errors in the past, so check the books before use.