Is there a solid strategy that you can apply to increase the chances of a win?
Of course the Eldritch Horror statistics do help in working out what can go wrong/right. But they do not offer a specific strategy -- if there is one.
My experience playing mostly 2-player sessions and one 4-player session has yielded a few tidbits that might help the starting player. I'll enumerate them below:
1) Do not obsess about keeping the world tidy, clear of gates, of monsters, of clues. Accept that it is messy and will just get messier. Think more about taking from it what's useful to you at any point in time. You have so few turns before that mythos deck runs out, before that doom counter reaches zero. Think of it like you're standing at the doorway of the shack in the middle of the pen filled with walking dead zombies. Bee-line it.
2) Make your optimal clue-gathering plan. Some characters are particularly effective in obtaining, dispersing clues, which are generally good as dice saving graces and often essential for mysteries. Assess if you have a better plan than simply "let's see where the clues fall and get there fast". Example: Use the spy's special action to generate clues every turn; keep a partner close by to hand them off. Move the Psychic one space over and park her in Arkham to try to get spells and score the Clairvoyance spell likely to make her a clue factory (and pair with her ability to send clues to players around the world).
3) Think about what your character does best and specialize. This might be obvious to seasoned co-op gamers, but became more obvious to me when realizing how fruitless it was to try to clean the board systematically and how much more useful it was just to tune out what a creepy bug in south america is doing at the moment. Take the politician; just sit in San Francisco with him for the first 2 or 3 rounds acquiring assets for your fellow team members and make the best of boosting their stats and equipment as early as possible where it will give you the best return.
These are only a handful of observations from 5 play throughs (1st loss, then 4 wins with very few players and an even number at that since I suspect the odd numbered teams have a tougher time after looking at the gate/clue spawn rate on the reference cards). The takeaway is to make an initial specialized plan and then reassess 2 or 3 rounds in because, at that point, you probably have acquired assets, conditions (hopefully blessed), and spells that require you to shift your strategy to fully optimize your best chances of winning. Stay nimble in that regard.
First and foremost, the goal is to solve mysteries. Thus, you first thought should be "How can I further that?" Otherwise, here is an ordered list of potential good moves:
This is based on a limited set of games (probably a few dozen or more) but helped by the statistics found in the question.
Note that none of the expansions (I have them all) have so far altered this ranking.
I've found that certain characters do provide benefits in certain scenarios. Some of their abilties really can be game winners such as the shaman's ability to manipulate the gate stack. It's also becoming clear that different tactics are required for different Great Old Ones. We have mastered Azathoth with an all round mix of characters and tactics but we are currently battling Yog Sothoth and it seems a more Lore and magic heavy approach is required. Likewise Shub Niggurath seems to be monster heavy so some real brawlers with serious weaponry will be required for that particular black goat of the woods.
Happy Hunting and be careful out there.