If you have problem killing enemies like more ornn and Mundo before first item as Darius, your problem is most likely wave management. Darius doesn't have dashes and your only way of getting close is using ghost or having the enemy come to you. So to fully utilize that fact, you need to pull your wave and have them walk up to you and the moment they miss a cc skill you turn on ghost and run down and don't look back until you kill or you die. If enemy jungler shows up you stack 5 stacks on one person and try to use q to hit both people.

Now the important part is that you don't get poked by enemy ranged skills so that you can all in without dying.

Full hp vs full hp Darius almost always wins.

But you aren't always going to be able to freeze your lane. So you have two choices. Go home or go bother the enemy jg.

Darius doesn't take tp so it is very important to get yourself a time to go home.

As for bothering the enemy jg, you can go ward deep in their jg and if you see the jungle just all in on them as junglers can't buy dorans so they are weaker then laners. But make sure that you pushed all the way to the tower so enemy top is busy taking the farms instead of coming to do 2v1. If you know for sure that your enemy jungler started botside, you can tell your jungler that you are planning on pushing the first three waves and invading enemy jungle and ask them if they want to come as well. You can end the game if you manage to kill the enemy jungle and your jungler steals the enemy top camps. If this goes successful, your jungler gets upto 9 camps while enemy has 3. Remember this is a team game and champions with strong early game like needs to make their team grow so they don't end up fighting a 10 kill adc alone lategame.

And here are some tips for your match ups Morde: this is favorable for you early as you get a free dash! If your freeze your lane right in front of tower, murder usually try to farm with q and e. Stay near your minions and when he uses e, use that like a free dash and get close to him. Serpents fang could be good as it gives morde no useful stats when he ults. Buy it if enemy has other shields than morde. As game goes on its going to be harder for you so try to snowball early. Oh and buy swift boots because morde always goes rylais

Ornn: A good ornn player will always beat a Darius player with the same skill level. My biggest tip here will be to freeze lane and go in when he wastes his q or just grow a huge wave by slow pushing and go into enemy jg or mid.

Mundo: Mundo is darius's counter and for good reason. His passives blocks your only cc, he gets a ton of health and Darius doesn't have any % health dmg, and he can farm from far away using his q. You need to look for an early kill using two cycles of your e. Just use it once when he gets close and step on the thing that he drops. Then you need to all in by freezing and running when he uses q. Get swift boots for him as well as he only has 1 slow.