I have never played as the Odrysians, but I will give it a shot.
But for now, until I can report my own findings, I can still offer you an advice in what works best for me when I try to expand.
Expansion is much like a battle. In a battle you try your utmost best not to be flanked. This is the same with expansion, you try to ensure that your kingdom is not flanked, the best way to do this is to make sure your kingdom is secure on 3 of 4 directions, i.e. to say if you are expanding to the West, the North, South and East should be free from threat. This way you can focus your army in one direction, and all your threats will come from one direction.
As the Odrysian, your frontiers are:
- North: he Getae, Bastarnae, Catiaroi
- East: The Black Sea
- West: Antogonidai, Tribalii
- South: Tylis
The East is safe. The West is the most aggressive, immediate threat. Threats from the North and South can be delayed for a while.
In the North, try to gain the support of the Getae and Bastarnae, as they share cultural affinity. They will not accept your offers but you can unite them against a common enemy the Catiaroi. Once they choose to fight against the Catiaroi, you should have a bonus modifier for having the same enemy. This way eventually you will be able to establish a Non-Aggression agreement. This should keep the North occupied with Catiaroi.
In the South, try to gain the support of Tylis by getting them to war against Bithynia. This should keep the South occupied with Bithynia.
In the West, Tribalii and Antigonidai. Tribalii are the easier target. Antigonidai are considerably harder since, they have a network of alliances. My suggestion to you is send an agent over to Sparta and Athens to get them to break-off from Antigonidai. Once, the network of alliances are broken you can begin your assault on Antigonidai and Tribalii.
How to expand?
This is very difficult since you are surrounded by enemies, meaning attacking with an army will leave your own settlement vulnerable to other factions. If you attack Tribalii, Antigonidai or even Tylis will take your capital, and vice versa. So the best strategy is to keep you kingdom small. It is easier to defend a smaller kingdom than to defend a larger one. Multiple fronts occur when the size of a kingdom is too great, therefore sharing borders with many nations that have many options and targets to attack. Try to weaken the enemy. Odrysian gain 50% reduction in mercenary recruits. This means you should take full advantage of mercenaries and disband them at the end of a turn. This means you will never have a standing army but you will have a better economy by avoiding an expensive military upkeep.
To get a sizable mercenary army your idea of economy changes. It is no longer important to have a higher income per turn that is required to maintain huge standing armies. It is rather better to have a bigger reserve. How to get a bigger reserve with low income per turn? It's simple! Sack! Sack! Sack! Kill off any enemy armies! Then retreat back to your region and activate ambush stance and replenish your troops, be sure to disband your mercenaries. If you can't retreat to replenish (check your movement range before you issue the order to retreat), then use raid stance to reduce any military upkeep. Basically dance back and forth in between choke points of your border.
Sacked it last turn? Sack it again this turn! Each sack gives your 1,500 to 3,000 denari that is more than the regular income of most starting factions. Accumulated wealth can be used to buy the loyalty of other neighboring factions.
Soon enough your enemies will spend more time spending their limited income on repairs and raising new armies will be a lot slower. This is when you can concentrate on expansion knowing that the nearby factions are too weak from the constant raiding and sacking.
Last but not the least, you see a nation wiped out that is in close proximity to your location, try to liberate them and gain a valuable military ally. Say if Antigonidai wipes out Tylis, liberate Tylis and use them to combat the Antigonidai.
Get the Night Commander Skill!
Yes this is very important to wiping out armies and creating a huge numerical advantage. Especially when dancing between borders. Enter enemy territory pick one of their most vulnerable armies, activate night battle, defeat and route them, retreat back to your own territory, ambush mode, replenish. Repeat until there is no standing armies left.
Weaken a Settlement
If you can't win a siege, it is better to weaken the settlement the best you can. Begin the battle manually. Dump all your missiles on the defenders and then manually retreat. This way you save your army from massive casualties while take a free hit at the enemy. Return again the next season and repeat.
*Disclaimer: I have not personally tried the Odrysian campaign yet and do not guarantee this will work. But I am sure it will help out a bit in your approach. I also haven't tried the Weaken a Settlement as I never had to. But I think if the game presents a tough to crack garrison, I could very well see myself employing such tactics!