Why is the upvoted, don't mean to be rude but your post is particularly unhelpful.

What you've said in your technical explanation is interpreted:

If you have two vectors representing position, and two vectors representing the orientation of your object, taken at sequential moments, for example consecutive frames, you can assign any average velocity given in both linear and rotational velocity vectors, and with the mass of something, and the moment of inertia tensor you have momentum of something.

This is incredibly ambiguous, and can be interpreted so incredibly wrong it is practically worthless, you've not qualified your descriptors, namely what belongs to what. I understand why you did this, a lot of this comes from colloquial speech patterns, or merely recalling something you once knew fairly well but don't really feel like going back and looking at your long lost text book or some 10 page explanation of kinetics to refresh yourself on more specific info, but I don't think this comment will be all that helpful to someone whose even passed basic college physics.

I'm going to attempt to make your technical answer, which is actually the only answer you gave to the question, saying that you need something is not an answer to how to do x process, only that you need process x in order to do x, and your technical answer would be the answer that explains the process for x.

lets start off by saying you have these two vectors given to any object with in your game, one for the position of your object, and one for the orientation. Taking a sample of these values at consecutive times while swinging your sword you can get an average velocity, much like averaging velocity based on two positions given in time, for example, the average velocity moving 300 meters north to south over 100 seconds is 3 meters per second (south). The problem with our situation is that we are swinging the sword, so in addition to linear motion, it has rotational motion. If our sword only had linear motion applying some force on an object, it would be as if you pushed the sword out rather than swung it, you would not be using movements in your joints to move the sword.

Knowing the rotational velocity, linear velocity and knowing the mass we are able to calculate the moment of inertia Tensor, which is a linear transformation which we will apply to our average angular velocity, which will result in the angular momentum we need for an object. But this is only the angular momentum we impart to any secondary object, we need to also relate this to the linear momentum, which is mass * linear velocity, which we can relate based on the equations here https://ccrma.stanford.edu/~jos/pasp/Relation_Angular_Linear_Momentum.html which is also amounts to angular momentum/ radius of angular movement.

To actually impart this momentum however you'll need to brush up on your physics, places like this

you have two vectors representing position, and two vectors representing the orientation of your object, taken at sequential moments, for example consecutive frames, you can assign any average velocity given in both linear and rotational velocity vectors, and with the mass of something, and the moment of inertia tensor you have momentum of something.