Neural Nets: unordered sets of ordered tuples as features of data
Your features are already numerical, so you can simply pass your array of numbers into a MLP.  For instance, if you have 5 sets of (x,y) coordinates per sample, your MLP will have 10 inputs.

One-hot encoding is used to convert categorical features into numerical values.  This image from Kaggle does a great job of illustrating how you might use one-hot encoding:



If you were to directly convert categorical values to numerical values, that would imply that one color is greater than another, so we need to use a boolean array instead.



As for the variable length feature vector, it is difficult to give an exact answer without knowing more details about your problem, but here are general possible solutions:


use a recurrent neural network
use distance-based regression/classification algorithms such as k nearest neighbors
transform your data into feature vectors of fixed length (which may not be reasonable depending on your data and what it represents)




A quick high level introduction to neural networks might be helpful.