Honour has different meanings from one area to another as well as from different periods in history. The samurai ideal of honour is very different to the Teutonic, for example.
Culturally speaking, honour can be defined loosely as "what is good for the tribe." Again, this is only a very loose description. Cultural honour differs between male and female, young and old. For example, a man avoiding conscription in modern United States is generally thought of as a coward, lacking honour. A female isn't even required to register for the draft, the standards for female honour are completely different. In the same way, a child in Western civilisations is not expected to fight and neither are the elderly. They contribute to the tribe in different ways. Telling the truth, doing "good" things, are mere sideshows. A person who is honourable is believed because the monkey brain realises that a person who has risked their life for yours should be trusted. Not the other way around.
Again, honour is different in even similar countries and regions within that country. Certain parts of the United States, Texas springs to mind, expect that a household owns a firearm. Australia, as similar as it is to the US, generally frowns on people owning guns.
Way back in the day though, Honour was everything to the tribe. A small clan that was made up of men who refused to defend the perimeter would quickly be killed, it's women enslaved and children murdered. Reference the entire history of the world for examples of this. A man who would happily kill anything that crossed his tribe was an incredibly useful asset to that tribe and would be considered honourable by his own people. He'd be lauded by all and probably made chief. A woman from that same tribe who risked herself by getting into endless fights would be strongly discouraged from doing so for biological reasons. Long term survival means children, only females can create children. It would be suicide for this tribe to risk it's future by allowing it's women to fight off hungry bears, wolves and men.
Fast forward to today and the landscape is completely different. That same man who kept his clan alive a few thousand years ago would be rotting in jail now for the exact same behaviour. That female who wanted to go to war ends up a hero for even attempting, see the recent hubbub about the two females in Ranger school.
Honour is about culture at the time and for those who it is important to, it is everything. The levels of suicide among veterans relate to this. They've come from an environment where that barbaric war chief would once more be a god amongst men. Then they come back to civilian life and are slapped in the face with the fact that, far from being conquering heroes, the people they believe they fought for revile them and everything they did. Cut off from their comrades, the fighting, the day to day routine that has been everything to them for so long... What other option do they really have? Their lives no longer have any honour, any worth. Why stick around when it's never going to get better?
Bringing it back to this book and with my apologies for the long post, Adolin murdering Sadeas is perfectly honourable. Saudis just told him that he's going to undo everything Dalinar fought for, start a civil war, murder his father and the King. Faced with that, what idiot would just let Sadeas go when it all could be prevented then and there? What other option was there, let Sadeas kill Gods know how many people and start a war that would damnation the world? Bad option that, not really honourable to let everyone die.
Kaladin fighting the Parshendi is also the epitome of honour for him. These are people that are killing your comrades, shot at him how many times and killed King Gavilar. It would be risking the safety of the tribe for him not to fight. This is why Kaladin gets the greatest honour "level up" for lack of a better term after the battle for the tower and in the defence of the King. Doesn't matter if it's a bad king, its your King.
Modern definitions of honour cannot be applied to historical events. By historical standards almost nobody now has any honour anyway. By modern standards, our history was filled with murderous psychopaths.
Stopping now, could go on for days.