Since

As a conjunction since means ‘from and after the time when’.

I have never seen him since I left school.
Many things have happened since he died.
We have been living here since I was a boy.
It has been raining since we reached the city.

Note that when since is used as a conjunction denoting time it should be preceded by a verb in the present perfect, and followed by a verb in the past tense.

Since can also mean ‘seeing that’, ‘as’, ‘inasmuch as’ and similar ideas.

Since that is the case, I will excuse you. (= As that is the case, I will excuse you.)
Since it is raining, we can’t go out. (= As it is raining, we can’t go out.)

OR
The conjunction or is used to introduce an alternative.

You can have tea or coffee.
We can wait or we can go.
You may take this or that.

Or can mean otherwise.

You must study hard or you will not pass.

In some cases or can be used as an equivalent to and.

They were not wanting in strength or courage, but they were poorly motivated. (= They were not wanting in strength and courage but they were poorly motivated.)

If

If can mean ‘on the condition that’.

If he comes we will meet him.
If you ask, he will help.
If you heat ice, it melts.

If can also mean ‘admitting that’.

If I am blunt, I am at least honest. (Admitting that I am blunt, I am at least honest.)

If can mean ‘whether’.

I asked him if he would come.
I don’t know if she is interested in the offer.

If is also used to express wish or surprise.

If only I knew!

That

As a conjunction that is used to express a reason or cause.

He was annoyed that he was contradicted. (= He was annoyed because he was contradicted.)
She was upset that he didn’t write to her. (= She was upset because he didn’t write to her.)

That can express a purpose.

We eat that we may live.
We sow that we may reap.

That is also used to express consequence, result or effect.

He was so angry that he tore the letter up.
She was so weak that she sat down to rest.
It was so late that we didn’t go out.

Than

As a conjunction, than is used with comparative adjectives and adverbs.

She is taller than her husband.
Wisdom is better than riches.
I love you more than he does.

While

While means ‘during the time that which’.

While you were playing I was working.
While there is life, there is hope.
The boys sang while the girls danced.

While can also mean ‘whereas’.
While he is hard working, his brother is quite lazy.