EDIT
A recent update has started listing what the enemies strongest color is in parenthesis in the description of the power in battle, so this is mostly not needed anymore. But there are some glitches and sometimes doesn’t get it right, so the information below can still be used to help determine strongest color if the game is telling you something that is wrong.
Certain abilities (4* Wolverine’s 
Surgical Strike being the most common) target an enemy team’s “strongest color.” (EDIT: See below for list of abilities that this applies to.) Ever have a SS go off and hit the wrong color doing half as much damage as you thought it would, failing to kill off that last enemy? It’s frustrating, but don’t let it happen again! Here is how you determine strongest color:
General Tile Strength:
When you tap on a player icon their info screen pops up detailing their abilities, if you hit the arrow by the abilities it will switch to a diagram showing all the tile colors with a number next to them - this number represents the tile strength for that color (also the amount of damage done for each matched tile of that type by that character i.e. with their icon on it). If you hit the arrow at the top by the character you can sroll through all the characters to determine who has the largest number. Whatever color has the highest single number is the strongest color. Only the highest single number matters, you DO NOT sum the strength of a color from all characters. So if three characters have a strength of 50 in red, but one character has a strength of 51 in blue, and no other character has a strength of 51 or higher on any color, then the strongest color will be blue. If the highest number is shared by two characters then tiebreaker rules apply (see below). Special Note: Pay attention to the Level of the enemy (shown in the upper left under their name when looking at their power/damage screen). Sometimes two characters will show the same number for tile strength, but be different levels. In this scenario the character with the higher level will be stronger regardless of position. This is due to the function they use to calculate tile strength based on level keeping the decimals, but hiding them and rounding down. So a level 131 will have a strongest tile strength of 65.6, and a level 130 will have 65.3, but both are rounded down to 65. This only seems to apply to character of the same tier. An overleveled 1* lvl 200+ character in PvE might not actually be stronger than a slightly lower level 2* character - the scaling is goofy there.
Goons:
Goons will almost always have the exact same strength for all colors, if this is the case a particular goon’s strongest color is determined by the color of the first ability listed (the ability on the far left when looking at their descriptions).
In your roster:
When you look at characters in your roster, usually (thanks to TxMoose for pointing out some exceptions below) their strongest color will be the top color flag (primary color), second strongest in the middle (secondary color), third strongest at the bottom (tertiary color). This convention is followed on the forums when people list character builds. So for example XFW appears as:
and if you look at his tile detail page you will see that green is his strongest color, followed by black, then yellow. And when people say their XFW is optimally covered at 5/5/3 it means he has 5 green, 5 black, and 3 yellow. Characters at the same level will always have the same strength in their primary color (note: this does not apply to 5* characters).
Tiebreakers (when picking YOUR team):
If two characters have the same strength in a color, the tiebreaker is their position when selecting them. When picking your team you have a middle spot, a left spot, and a right spot. The strongest character is in the middle, next strongest on the left, third strongest on the right. Tiles will bear the symbol of the strongest character for that color. For example: When using Hulk/Patch you want Hulk to make your green/red/black matches so you would put him in the middle with Patch on the left or right. Or in a PvP where the required character is in the middle you would put Hulk on the left and Patch on the right. When you first go in to battle, before you make a single match your strongest character will be up front (right of screen), followed by your weakest character in the middle (think of that character being protected by the other two), then your second strongest in the back (left of screen).
Tiebreakers for enemy team (when looking at a node):
When you first tap a node to see an enemy team it will show you the characters and their levels with the strongest character on the left, weakest in the middle, and second strongest on the far right. When you hit the fight button this first time it takes you to the boost screen:
Tiebreakers for enemy team (when looking at the boost screen):
On this screen the strongest character will be in the middle, second strongest on the left, weakest on the right - just like when you select your team. If you tap on the individual characters here it will bring up their abilities (a great place to learn about the cover strength of a team before you fight them, and give you an opportunity to back out of a match with an optimally covered team that is underleveled or something like that).
Tiebreakers for enemy team (in battle):
The only way to determine tiebreakers for the enemy is to notice their orientation before they make any matches. So when a new team loads in for a survival node, pay attention to where they are at first, and note the strongest characters. Here they are oriented as a mirror of your team in battle - strongest up front facing your team (left of screen), weakest in the middle, second strongest in the back (right of screen).
A little more info: https://forums.505go.com/discussion/comment/321061
Please let me know if I missed anything, or if I can clarify something. Thanks!
EDIT: Special thanks to Phantron for pointing this out…
Some abilities that use “strongest color” use the tie breaker method outlined above, we will call this deterministic. Other abilities do not use a tie breaker, but randomly select one if there is a tie. Below are the methods and which abilities use each method. Please help me to fill in abilities that are not listed or incorrect.
Deterministic Abilities:
Surgical Strike
Countdown for What
Random Abilities:
Master Plan
Nightstalker
