UNLESS, IN CASE, PROVIDED THAT, AS LONG AS, SO THAT

If, unless, in case, provided that, as long as, so that

1. If and unless
Unless means the same as if ... not. It always refer to the conditional part of the sentence and not the result part of the sentence:

If he doesn't get here soon, we will have to start the meeting without him.Unless he gets here soon, we will have to start the meeting without him.

We often use not + unless, which means only ... if, when we want to emphasize a condition:

They will only sign the contract if we give them an additional discount.They won't sign the contract unless we give them an additional discount.

2. If and in case
We use in case to talk about precautions we will take before a problem happens. We use if to talk about what we will do after a problem happens:

We are going to insure the shipment in case the goods get damaged in transit.
(We will take our insurance first; the problem may or may not happen afterward.)If the goods get damaged in transit, we'll make a claim.
(The damage may happen, and we will make a claim afterward.)

Note that that in sentence with in case, we often use going to rather than will because we are often talking about something that we have already decided to do.

3. Provided that vs as long as, etc.
We can use provided that/providing, as long as, and so long as when we want to emphasize condition. Provided that and as long as mean if and only if (providing and so long as are a little less formal):

I will agree to these conditions provided that they increase my salary.
(I will only agree if they give me more money.)
The strike will be successful as long as we all stay together.
(It will only succeed if we all stay together.)

4. So that
We use so that to say what the result or purpose of an action will be:

I'll take a credit card so that we don't run out of money.
(The credit card will stop us from running out of money)