Small question regarding a monk’s martial arts when combined with shape changing that retains class features. If I have a monk that has some way to change shape, does martial arts apply to something like a raven’s beak attack, allowing me to do martial arts damage instead of a flat 1?

Some natural weapons can be uaed as unarmed strikes but i dont think such monster's action can. 

I believe Plaguescarred is correct and Sage Advice covers this with:

What actions can monsters use to make opportunity attacks? Are Multiattack and breath weapon actions allowed?

A monster follows the normal opportunity attack rules, which specify that an attack of opportunity is one melee attack. That means a monster must choose a single melee attack to make, either an attack in its stat block or a generic attack, like an unarmed strike.

However a DM might need to make some rulings that allow for certain natural weapons on a creature to do some additional or alternative damage from bludgeoning to best reflect an unarmed attack by a creature that could likely do so such with claws, maw or tail/stinger.  I think there's definitely some room for a player to negotiate if they've been True Polymorphed or such.  Some rules that might help while I was looking into all this:

 PHB 195:
"A melee attack typically uses a handheld weapon such as a sword, a warhammer, or an axe. A typical monster makes a melee attack when it strikes with its claws, horns, teeth, tentacles, or other body part."

"Instead of using a weapon to make a melee weapon attack, you can use an unarmed strike: a punch, kick, head-butt, or similar forceful blow (none of which count as weapons)"

Of note is the term "or similar forceful blow" which suggests a monster's natural weapons would have to do bludgeoning type damage.  BUT, if we take inspiration from character race classes such as lizard folk's "bite" - "You have a fanged maw that you can use to make unarmed strikes. When you hit with it, the strike deals 1d6 + your Strength modifier slashing damage, instead of the bludgeoning damage normal for an unarmed strike."

We can take this one of two ways:
1. Inspiration that beasts and other creatures that can attack with body parts that deal non-bludgeoning type damage can be used as unarmed strikes
2. Confirmation that bludgeoning damage is normal for an unarmed strike to be considered such unless specified as otherwise in the rules such as lizard folk's "bite".

Then we have MM P10:
Actions:
When a monster takes its action, it can choose from the options in the Actions section of its stat block or use one of the actions available to all creatures, such as the Dash or Hide action, as described in the Player’s Handbook.

Jeremy Crawford has also acknowledged that there's a bit of a loophole with natural weapons that are both unarmed attacks AND weapons giving us RAI natural weapons are not weapons but RAW they are:
https://twitter.com/JeremyECrawford/status/996549348140826624
"I'll boil it down for you. When we wrote the "Player's Handbook," we meant the weapons on the weapon table when we wrote "weapon," unless we said otherwise. But you break nothing in the game if you let natural weapons go along for the ride."

EDIT: Be careful about  a monster's "multi-attack" as it often specifies the exact attacks it can take as being the listed ones, not giving the option of generic attacks outside their stat block

So I wouldn’t be able to do martial arts damage for my raven’s beak example, but if I did something like a talon strike (which isn’t listed as an action) I could apply martial arts?

Yes a raven can make unarmed strike with its beak, head, talon, wings or any other body part as described in the PHB.

The Raven is a bit of an odd example as its natural weapon does less damage than a Monk's Unarmed Strike. Usually when this question crops up it is about a Natural Weapon that does more damage, like a Mammoth.

All creatures can make an Unarmed Strike using their body following the normal Unarmed Strike rules. When it comes to Natural Weapons, they cannot normally be used to make Unarmed Strikes. Many player races that have Natural Weapons have specific language that allow them to be used to make Unarmed Strikes, like a Tabaxi's Claws or a Lizardfolk Bite. However, there are also Player Natural Weapons like a Dhampire's Bite or the Path of the Beast Natural Weapons that instead also count as Simple Weapons and cannot be used to make Unarmed Strikes.

Ultimately though this is something to bring up to your DM as they may not be aware of these peculiarities or may want to play it differently.

If we're talking about the effect of a Shapechange or something similar, then I would say that the "provided that your new form is physically capable of doing so" caveat disallows applying Martial Arts to any form that doesn't have the same basic arrangement of limbs as your original form. You get the improved damage die because you've drilled in performing specific effective moves, so while I'd say you could use them in the form of a gorilla or troll or something else in that vein, anything with a different arrangement wouldn't be compatible.

Most other shapechanging effects like Polymorph specifically say your actions are limited by the new form, which means for attacks you can make the attacks printed in the block or a generic Unarmed Attack.