Multiclass classification of timeseries data using NN
How to approach the solution using a NN ?

Given your data, it doesn't look like an RNN/LSTM is the most sensible choice.

It looks like you have two features and a binary output. RNN/LSTM are useful with variable-length input, otherwise, they are a bit overkill.

Also, make sure that you have a reasonable amount of data before using a deep learning approach. They usually have many parameters to train, and if you don't have enough data points, this might be difficult to do.

If you want to stick to NN, I'd say a regular multilayer perceptron might do the job. If you are open to other options, I would try decision trees for this particular problem.

How do I convert the categorical value of OUI to numerical entities

You could use one-hot encoding. There are plenty of implementations out there (i.e. scikit-learn), or you could do it yourself.