Calculations for the elemental damage multipliers:

In Runersia, you need to compare each color in the skill/spell orbs and attack orbs (considered as a whole) with each color in the target's defense orbs (including a "null" color with 0 orbs for any side without elemental orbs). Now the relationships between the elements are not only green > blue > red > green, white > dark > white (which elements are strong against others); but also green < red < blue < green (which elements are weak against others). You add the number of orbs if the colors in the pair oppose each other (then multiply that by 4% if the attacking side has the advantage, or by -4% if the attacking side has the disadvantage), and subtract the number of orbs otherwise (then multiply that by 2% if the attack has more orbs than the defense, or by -2% if the attack has fewer orbs than the defense). Sum all those percentages, add 1 to the result, and that's the elemental damage multiplier (the final damage is rounded up after applying that multiplier to the base damage). In the case of skills/spells not targeting an enemy (such as heal), it would appear that only the attack orbs are taken into account (giving you a bonus of 4% per attack orb). In the best case scenario, your damage can be increased by 84% (when your 3 skill/spell orbs and 9 attack orbs trump 9 defense orbs, since (3+9+9)*4% =  21 * 4% = 84%), or be decreased by 84% in the reverse case.

Also, it's interesting to note there aren't same-element resistances anymore (you get resistances when getting attacked by orbs which have disadvantage to your defense orbs, or when your have more non-opposing defense orbs - for each element - than the attacker's skill/spell and attack orbs). As an example, here's the damage calculation for Jiu's Divine Ray (3+3 = 6 white orbs on attack) against Avenir (2 white orbs on defense), which happened at 2:06:27 : round_up(198 * [1 + (6-2) * 2% ]) = round_up(198 * 1.08) = 214. In GE, that multiplier would have been 0.67 (instead of 1.08) because of the same-element resistance (thus reducing that damage to round_up(198 * 0.67) = 133).

Here are other examples for the damage calculations:

For a Frost Dragon's breath attack (against different units):
(4 blue vs. 0): round_up(131 * [1 + (4-0) * 2% ]) = round_up(131 * 1.08) = 142
(4 blue vs. 1 white): round_up(131 * [1 + (4-1) * 2% ]) = round_up(131 * 1.06) = 139
(4 blue vs. 2 white): round_up(121 * [1 + (4-2) * 2% ]) = round_up(121 * 1.04) = 126


For Grados's Judgement attacks (against different units):
(6 white vs. 1 green): round_up(257 * [1 + (6-1) * 2% ]) = round_up(257 * 1.10) = 283
(6 white vs. 1 dark): round_up(272 * [1 + (6+1) * 4% ]) = round_up(272 * 1.28) = 349


For Jiu's Divine Ray:
(6 white vs. 1 dark): round_up(224 * [1 + (6+1) * 4% ]) = round_up(224 * 1.28) = 287


For the Elemental's breath attack (against different units):
47:21 (0 vs. 1 green): round_up(72 * [1 - (1-0) * 2% ]) = round_up(72 * 0.98) = 71
53:51 (0 vs. 2 white): round_up(72 * [1 - (2-0) * 2% ]) = round_up(72 * 0.96) = 70


Examples for skills/spells not targeting an enemy (heals):
Heal: (caster has 1 white orb on attack): round_up (162 * [1 + 1*4%]) = round_up(162 * 1.04) = 169
Heal: (caster has 3 white orbs on attack): round_up (215 * [1 + 3*4%]) = round_up(215 * 1.12) = 241
Area heal: (caster has 3 white orbs on attack): round_up (143 * [1 + 3*4%]) = round_up(143 * 1.12) = 161


Examples with more than one color pair:

(2 blue vs. (1 red, 1 white)):  round_up(152 * [1 + (2+1) * 4% + (2-1) * 2% ]) = round_up(152 * 1.14) = 174
((1 red, 1 white) vs. 2 blue):  round_up(112 * [1 -(2+1) * 4% - (2-1) * 2% ]) = round_up(112 * [1 - 0.14] ) = 97
(4 white vs. (1 red, 1 white)) :  round_up(177 * [1 + (4-1) * 2% + (4-1) * 2% ]) = round_up(177 * 1.12) = 199 (this is an interesting example, since it shows how the elemental variety screwed the cyclops (1 red, 1 white) over - Grados's (4 white) multiplier would have been 8% if the cyclops had no defense orbs, or 6% if the cyclops had only one white or one red defense orb)
((1 red, 1 white) vs. 4 white) :  round_up(102 * [1 - (4-1) * 2% - (4-1) * 2% ]) = round_up(102 * 0.88) = 90
((1 red, 1 white) vs. 2 black): round_up(146 * [1 + (1+2)*4% - (2-1)*2% ] ) = round_up (146 * 1.10) = 161
(2 black vs. (1 red, 1 white)): round_up(138 * [1 + (1+2)*4% + (2-1)*2% ] ) = round_up (138 * 1.14) = 158