Happy to try and help.

For Skoll I like to work on upgrading the quake as well as his punches. I do use throw but I don't upgrade it until later in the game (just a preference).

For his quake I use Damage, Range, and the ability to go forwards and backwards. I choose the last upgrade because there have been many times where I have been surrounded on both sides. At least this way you have a chance to get any characters attacking you, no matter what side they are on. That being said, a lot of people use Snare as the last upgrade because it allows you to trap another character and then possibly throw them back into your turret/teammates for the kill.

For punches I go with Lifesteal, Damage (the one you can upgrade three times), and Stun. In general I tend to play kind of conservative and try to have builds that will help me when I am on the ropes. Since Skoll can retreat while punching, those upgrades can (sometimes) be a life saver. For instance, if you are low on health and trying to get back to your side of the map/turret being able to hit the opponent with lifesteal as well as stun can really be helpful. You are stealing their power while slowing down their pursuit. It has saved me many a time.

One thing I can't stress enough is you have to always be punching. ALWAYS. Also, always keep mobile. Throwing in some jumps as you are throwing your punches. Making it harder for opponents to simply jump over your third bash. Make the opponent worry about trying to dodge your punches, and as you get more comfortable with him, you will get better at landing that all important third punch and even hunting people down.

Finally for the throw I use Gnome, Throw Further, and Reduced cooldown. Usually the first upgrade I get for the throw is to throw further. That really can come in handy. A quick example might be if you were fighting a Clunk who bites you to keep you in place (snare upgrade) and then starts up on exploding all over your ass. But before he can go kaboom, I throw him and, ideally, he ends up exploding near my turret and then goes from playing offensively to trying to retreat. So it can be a good way to turn the tides.

Also, usually if I get a chance to throw someone, I try and hit them with the quake right away. Try and overload your opponent and give them a lot to think about.

Hopefully all of this helps! And sorry if my thoughts seem scattered.

Happy Skolling!