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I find my Leman Russ battle tanks and infantry getting mowed down by fire prisms, harlequins, farseers, and DIRE AVENGERS.
Any Advice?

There is some variance depending upon what points value you are playing at and your normal army composition. Some suggestions all the same:

If the Farseer is a problem, bring a Daemon Hunters' HQ Inquisitor with the Psychic Hood. Only works about a 1/3rd of the time, but it can slow things down. Keep in mind that per the FAQ Mind War can now be stopped by cover saves-that helps with some sniping issues. You could also throw on a Null Rod and bring along some Heavy Bolter servitors to solve your Harlequin problem.

If he is investing lots of points in Bright Lances to undo your AV14, spam some Hellhounds. Just as hard for him to destroy, and they deny a cover save. Give that so much Eldar armor is 4+ or worse and covers prevalance in 5E, you should come out well. Hellhounds will also destroy Dire Avengers for the reasons cited above.

If your troops are getting shot to pieces by small arms fire, cover and Chameleoline is your best solution.

Fire Prisms . . . take your pick of Autocannons, Lascannons, preferably in Platoon HQ support squads, or some deep striking Meltagun veterans. Any of them should get the job done.