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I'm not at all experienced in the game, but from my occasional playing of the game, I have come to understand a few key elements to Anhur.
Lane a bit at the start and start clearing the jungles when you feel you can clear them fast enough. Don't waste too much time in the jungle, it's not worth it.
Gank. Participate in team fights. Watch the map. Use third-person view as your advantage.
By this time, you should be unstoppable. Don't make mistakes, don't get too cocky. Push some lanes if needed, but your presence must be in team fights.
Focus on the squishy people. Clean up later.
Anyone that has a brain and can play is a good partner.
If you're good, you won't let anyone counter you.
This will make you strong. Done. Just kidding, you need to be able to read the situation. There is, I repeat, no set build order.
PS. I have no clue about ability order either. It's all up to you.