Early game with OotMM is always hard, you need to thin well about every single step...
1) I would recommend to bring down Imladris as early as possible, that should give you some rest at least from the High Elves for some time - now you can focus totally to the east.
Try to keep peace with Eriador as long as possible, if necessary give them maps, they don't cost you anything.
2) Next step should be to take the rebel settlements Framsburg and Wrakyaburg and concentrate your forces in Wrakyaburg - from here you can defend against offences from the Sylvan Elves as well as helping out Dain's Halls if it is sieged by the dwarves. In siege defences against dwarves never rely solely on the fight at gates and walls, dwarves will always be superior in melee on little space. Bring out snagas through the side gates and pepper the flanks of the dwarves advancing towards the main gate with javelins, attack them from all sides once you run out of ammunition.
3) I managed to bring down the only two dwarven family members Dain and Thorin in an early invasion towards the Iron Hills - if you can achieve something similar, it would be very helpful of course...
4) Take the two well-developed settlements in Lothlorien. I'm not going lie to you, it's going to be really hard. Use many archers and always use them with flaming arrows - that way you can at least partially substitute their inferiority. Even elven archers have a hard job vs. mass-flaming-arrow-crossfire. Otherwise spread out your formation wide and try to engage them in melee with superior numbers (opposite with the dwarves, always harrass them with arrows and javelins).
5) Once Lothlorien is down, the Sylvan elves mostly use their fighting spirit. Now you can build up, soon there should be trolls and wargs available which solve most of your problems. Now you can freely choose whom to attack next, depending on how the campaign plays out, you shpuld be able to match all of them.
This way it worked for me - of course every campaign plays out different, so I can't guarantee it to work...
PS:
It should look more or less like this in the end...