Half-Orcs can get Great Weapon Aptitude (+6% magical on glancing blows), +4 damage with THW, +3 PA, +2 Strength while raging, +2 Strength at character creation, and +2 Strength from enhancements. Additionally, Half-Orcs can get +3 Action Boosts, which can be very important for certain classes.
Warforged can get Great Weapon Aptitude and PA.
Dwarves can get +2 damage with OH axes and +4 damage with TH axes.
Hence, for one-handed weapons in the main hand, all other things being equal the order will be Half-Orcs with rage (6), Half-Orcs (5), Warforged (3), Dwarves with axes (2), where the numbers given in parentheses are the bonuses to damage. How much DPS this works out to depends on the weapon base, class, rate of attack, and target, but you will get at least 3.5 trash DPS for each 2 damage bonus on any reasonable melee choice. Hence, we would expect the gap between raging Half-Orcs and raging WFs to be at least 3 * (3.5/2) = 5.25, or about 1% DPS with good gear at level 20. Because this is a flat difference, the relative difference is more pronounced at earlier levels. The gap to Dwarves is harder to establish because Half-Orcs and WFs would probably not be using axes.
For two-handed weapons without magical processes, the order will be raging Half-Orcs (10), Dwarves with axes (4), Warforged (3). The choice for this field is obviously the eSoS, though, so Dwarves are really a (0).
For two-handed weapons with magical processes (such as Lit II), Half-Orcs are still clearly on top, and Warforged with axes almost surpass Dwarves with axes. 75% glancing blow rate * 6% process chance * 19/20 hit chance means that the magical processes need to do more than 23.39 damage to make up the 1 difference. 1d6 shock + 2d6 holy + .015 * 600 lightning strike + 2 * 11 / 19 shocking burst + 2 * 11 / 19 shocking blast + 14 / 19 shocking blast = 22.55, so not quite.