[...] organization number for [...] combat troops [...]
[...] short supply [...]
As to organization, apart from the game difficulty settings it's only tech and generals that determine the max organization of an army, IIRC. Not having a general command your troops is a flat -20% org, although i am unsure whether this is added to or multiplied with the base org and tech bonuses. Additionally your national stockpile slider determines the max org possible for your troops, so if fighting equal teched enemies you have to go 100% stockpile and also be able to fully supply your troops, either through your own industry or by acquiring the needed materials from the world market. Although being able to fully supply your troops (with max nat stockpile) might just play a role in regaining org not in its max value.
It also might just seem that your enemy has better organization than you if you are taking the wrong stance on fighting your enemy in a given period. In combat between uncivilized countries i feel that attacking is the only viable route, whereas fighting between civilized countries up to and especially with machine guns a much more defensive approach is advisable, unless you have a definite tech advantage or feel the expenditure of countless lives justifies your goal and is sustainable.
The org loss in combat is tied to the attack/defensive stats of the engaged unit types, depending on which side is doing the attacking/defending. Until and including machine guns defensive has the advantage in most cases and thus a defending army is more likely to inflict hefty org (and of course strength) losses, whereas the attackers will inflict less casualties on org/str with comparable die rolls in their favour.
These defensive stat advantages are amplified by defensive die modifiers like dig in bonus and terrain bonuses; with the general's attack/defensive attribute adding more to that. So, until you research bolt-action rifles, if you have the numbers be sure to also have a general with attack bonus and do your attacking in plains without crossing a river and at least one of cavalry/hussars/guards to reduce initial dig in bonus, else just lure your enemy into defensive battles by baiting the AI with small stacks and moderately reinforcing these, all the while keeping the upper hand, so it pours more troops into that particular battle. With bolt-action rifles you can relax a bit and act more offensively, without gambling of course, as attacking a fully dug in tech-equal enemy in fortified mountains across a river is still not the smartest thing to do.
Regarding supply - the attrition kicks in the moment the supply needs of all regiments in the province, no matter how they are organised (i cannot remember ever seeing a general that reduces supply requirements), exceeds the province's supply rating. If you select an army in a province and mouse over the attrition number in the upper right of its details the game will show you an overview of the supply needs of all the troops stationed in that province with a breakdown of the province's supply and additional factors influencing it (additional supply requirements for mountains/jungles/adjacent hostile forts if in war). The medicine tech is a must have because its inventions reduce the supply needs of your units for up to 25% with all inventions acquired, i.e. a stack of 24k will then only require a supply rating of 18 instead of 24 without these inventions.
If your attrition is greater than 0% all your units loose soldiers depending on how far above the province's supply rating you are up to a maximum percentage. If your reinforcement rate, which is also muddily detailed when mousing over the attrition percentage in the unit details, matches attrition the troop numbers become stable.
Timber has started to be produced and I'm getting enough to build my naval bases 
