What are the difference between these 3 verbs?
It's easy to explain that with 'insert' there is usually a specific place where the object (data) is to be 'inserted'. How about for 'enter' and 'input'? Are there any major differences I should know about, or is my usual reply, "Both are OK in this case." the correct response?
Please enter the data and then press "OK"
Please input the data and then press "OK"

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I agree with Michael and Romulus as it's important to learn the most commonly used expressions.

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Hello Hisun,

to INPUT:

to ( insert) data into your computer.

to INSERT:
to put in or between

to ENTER:
to insert or intrdouce.

The 3 of them could be used actually ,
The more commonly used are :
to enter the data
to insert the data
You are not likely to hear " to input the data" ,although linguistically it is correct.

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We can say 'to enter' information, numbers, figures, details, etc. not only into a computer but also in a book, in a list, on a form, etc... 

However, we use 'to input' information (data, text, figures) to mean 'put information' into a computer. 

'To insert' has a different meaning. We use 'insert something into something else' to mean 'add something to a piece of writing': 'insert another paragraph into the essay'.

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Hello Hisun

in⋅put
–noun
1.    something that is put in.
2.    the act or process of putting in.
3.    the power or energy supplied to a machine.
4.    the current or voltage applied to an electric or electronic circuit or device. Compare output (def. 4).
5.    Computers.
a.    data to be entered into a computer for processing.
b.    the process of introducing data into the internal storage of a computer.
6.    contribution of information, ideas, opinions, or the like: Before making a decision we need your input.
7.    the available data for solving a technical problem.
8.    Scot. a monetary contribution, as to charity.
–adjective
9.    of or pertaining to data or equipment used for input: The keyboard is my computer's main input device.
–verb (used with object)
10.    Computers. to enter (data) into a computer for processing.
11.    to contribute (ideas, information, or suggestions) to a project, discussion, etc
      Something put into a system or expended in its operation to achieve output or a result, especially:
         1.
            Energy, work, or power used to drive a machine.
         2.
            Current, electromotive force, or power supplied to an electric circuit, network, or device.
         3         
Word Origin & History
input 
1793, "a sum (of cash) put in," from in + put. Computing sense of "data fed into a machine" is from 1948; the verb in the computing sense is attested from 1946. There was an obs. Scottish verb input (1498) meaning "to put in (prison, etc.)," but it died out long before this.

"in put" and "enter"verbs have same meaning...

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I would second romulus's response that "enter" and "input" are more or less interchangeable.  As a verb in your examples I would tend more toward "enter".