to… / in order to…. / so as to….

You are right, Gyonggu. If we use in order to it sounds a bit more formal and explicit than to by itself, but both are equally possible in both spoken and written English.

They both convey exactly the same meaning when expressing purpose:

• To cut the tree down, I had to hack through the undergrowth first.
• In order to cut the tree down, I had to hack through the undergrowth first.

In order to is normal before a negative infinitive. We do not usually use to by itself here:

• In order not to oversleep, I set the alarm for seven o’clock.
• I walked very slowly across the room with the drinks in order not to spill them. 

We can also use so as to instead of in order to and it carries the same degree of explicitness or formality:

• We moved house last year so as to be closer to our children and grandchildren.
• I gave him a cheque in advance to ease his financial problems and so as not to delay the building work.

Before stative verbs like know, seem, appear, understand,have, etc, it is more usual to use in order to or so as to:

• I talked to them both for half an hour so as to have a thorough understanding of the problem.
• I followed her around all day in order to know whether she had any intention of meeting him.

So that.../ in order that ...

These structures are also frequently used to talk about purpose, although so that is more common and less formal than in order that.

Note that these structures are normally used with (modal) auxiliary verbs.

Compare the following:

• He’s staying on in Australia for nine more months so thathe can perfect his English.
• He’s staying on in Australia for nine more months in order to perfect his English. 

• We’re going to leave by three so that we don’t get stuck in the rush-hour traffic.
• We’re going to leave by three so as not to get stuck in the rush-hour traffic.

• Jamie had an afternoon nap so that he wouldn’t fall asleep at the concert later.
• Jamie had an afternoon nap in order not to fall asleep at the concert later.

• In order that you may pass the exam, we recommend you read through all your notes. (Very formal.)
• In order to pass the exam, we recommend you read through all your notes. (Less formal.)

Note that in informal colloquial English, that may be omitted from the so that construction.

Listen out for this variation, though I wouldn’t recommend that you use it:

• I’ll come early so we can have a good chat before Denise arrives.
• I’ve bought a video camera so I can film the children as they grow up.
• We shall wear warm clothes when we go camping in October so we don’t get cold.