Depending on how friendly games your playing, and how competitive you all are, another approach is to ask them what they think you should be doing to stand a greater chance. Im only playing friendly games, and if we once or twice have had something very powerful hard to stop something, we also talk about how to counter it, and if we can't come up with something suitable that later on works, we let the powerful stuff stay at home. Which in this case, could be to let the High elf player understand that you don't find it that enjoyable being constantly beaten by his Teclics powered army.
Against skaven it sounds like you need some warmachine and missile unit hunters, Vargheist and bats are probably useful here. The shooting stuff in his army rarely have decent LD, and apart from him making a shooting hill with his warlord smack in the middle I guess they won't be using his LD either. So if you can get the missile units to take Terror and panic tests, they should not be shooting so much.
But yes more details on your opposition, what spell lores or just spells they really like to use. What numbers they bring in units and types and such. Together with your limitations, like if you don't have certain models forexample vargheists or you like hate playing with level 4 wizards in your army. Then we can help you much much better.
What you might find out, is that you might perceive Teclics and his unit as the greatest threat, and maybe he is. But it sounds like a very expensive unit, now im a wood elf player, so I would have most of my army dealing with the rest of his army, and chaff stuff making the white lions with Teclics move around the table where I want them, and away from the main battle where they can earn there points. I would be using eagles and dryads for that, im pretty sure you can do similar things with dogs, bats and summoned zombies. And let the rest of your army concentrate on everything else he has.
Im not that knowledgeble against skavens, but its clear you see the shooting part as the biggest problem, and I know skavens can shoot into combat. But again maybe its about taking the right skaven units out of the game, where you score important VP. And let him shoot all he want, but again more details, and im sure there is experienced VC generals that know exactly what to advice you on.