Druid during the daytime is an interesting one. Are they overconfident? Will they chase you indoors? Do they have charmies? Lets assume, for the sake of argument the second worst case scenario. You are rolling down Eastern Road doing your orc thing when boom! Druid with CoW and Treant. I'm specifically excluding the Hunt because the right answer is simply to run away at that point and running away doesn't get you kills.

The first step to any battle is being prepared. As an orc you should always have at least 2 natural weapons on you (non-metal) and one of them should, ideally, be a whip or flail. If you only have 1, that is ok, you can either remove your dual wield, or just suck it up that you aren't going to do great damage, just good damage.
As an orc, you should also have a slave (at the point where daytime druid matters, because sunray is dangerous).
Prot. vs align isn't going to help you, but if you have a stoneskin prep (use disease + damn instead of poison + hold) now would be a good time to eat it.
You have lots of blood on hand, right? Cause this is probably going to hurt.
Sunrays blind, but it can be cured, so pull any spare cure blinds out of your trunk.
You have been buying purple roots right? Because being able to fog an Outlander druid might come in handy if you get them spinebroken.

As a Shigru, the equation is honestly a fairly simple one... Can I get a rush off? My first step is enlarging. They are going to be armor of thorns anyway, so bashing won't do be any good, and they will probably be flying as well, so I want the best chance at landing a spinebreaker. Rush into them such that I seperate them from their charmies, and try for a spinebreak.

Spinebreak lands? Check if they are flying? No? Retrieve slave from previous room, trample, trip to death.
Yes? Ok, Go get my slave. Fog them if I can (and it is worth it). Make sure I have my natural weapons (as best I can) on. Trample, then lash. Chances are that without prot. vs metal in their favor I'm going to out damage them even with sunray working against me. Maybe they are prepped to the gills, or my lash misses so I flee, chug blood and repeat with at the rush step, ignoring the spinerbreaker step as my slave has run away and it gives me next strike unless I think I can catch a prep falling.

This is sort of a battle of attrition but orc outheals anything else, so you should be able to wear the druid down. If you *really* want to land the kill (and you have a polespec slave) you can try a desecration, and/or crushing assault. Druid melee doesn't frighten you, but sunrays hurt, so make sure you stay healthy enough to deal with them.

Once you get them on the run, rush + lash will work out greatly in your favor as druids (in my experience) are notoriously bad about carrying return/teleport potions and they think they can outrun anyone. Show them the error of their ways.

In the case that this is instead in a wilderness location and the druid has chamo (worst case scenario)... You can only prolong as far as your blood and their willingness to try things other than sunray will take you. Krunk fought a druid in the Tree to a standstill for something like 24 hours until the druid finally starting sunray-ing... then Krunk ran away. Can't keep them in the fight, can't keep them from healing (chamo) so there becomes no point. They can only kill you if you let yourself get sunray-ed to death, and you can't really kill them. Fight somewhere else next time.

As a non-Shigru, it is tougher, though you will have some other things working in your favor. Ideally you need to do one or both of the following: Damage them faster than they can damage you (Maumlauk with natural weapon makes this possible, if a bit unlikely), or blind them so you can fallback and avoid the sunrays (and CoW and Treant melee). Soot ritual or Dirty fighting will help with those, so it is really just a matter of getting the druid blind and a slave taking the blows. Then you lash until the druid realizes they aren't hitting you and flees. Once the CoW and Treant are out of the equation, you can proceed with the Shigru strategy (minus rush) of lashing them to death or hoping a prep falls. So long as you stay near full health and have some kind of saves, 2 sunrays aren't going to kill you outright, so you can afford to try, fail, chug, and try again for a bit.

If you can't get a slave taking the blows from CoW and Treant, and you can't handle their melee + sunray (you can't) run away, heal up, get a new slave and try again. The biggest thing to keep in mind is that they can't keep you in place. You are a hammer and need to turn them into a nail. With CoW and Treant their melee and sups are too much to handle, so you have to get that out of the way. Then it is a matter of having the right weapons and striking them where they are weak.