Why we need 1,2,4,8 bytes to store logical variable in fortran?

Question 1

First, Fortran doesn't say that we have logical types taking up 1, 2, 4 and 8 bytes each, and they certainly aren't logical(1), logical(2), logical(4), and logical(8). An implementation may choose to offer those, calling them those names.

A logical variable can indeed be of only two values. From the (F90, although F2008 says the same in a different place) standard 4.3.2.2:

The logical type has two values which represent true and false.

A processor must provide one or more representation methods for data of type logical. Each such method is characterized by a value for a type parameter called the kind type parameter.

[Emphasis here and later verbatim.]

For a logical type of default kind the rules of storage association (14.6.3.1) say that:

(1) A nonpointer scalar object of type default integer, default real, or default logical occupies a single numeric storage unit.
(5) A nonpointer scalar object of type [..] nondefault logical [..] occupies a single unspecified storage unit that is different for each case.

So, the compiler must offer a logical type which is of the same size as an integer and real type, but, equally, it can offer representations taking up 1 bit, 1 byte, or whatever. The kind number, and size, for any given representation (hence my first paragraph: the question isn't universally valid) is implementation-specific. That said, there is no SELECTED_LOGICAL_KIND (or such) intrinsic.

As to why multiple representations can be useful, that comes down to offering a choice, perhaps for special cases such as for arrays and ideal memory management (some people like to play non-portable tricks). However, memory access/alignment requirements suggest that a scalar logical would be at least one byte (or padding make it the same). For C interoperability (F2003+) there is a kind C_BOOL corresponding to the companion C processor's _Bool, which needn't be the same size.

Question 2

LOGICAL

The FORTRAN standard requires logical variables to be the same size as INTEGER/REAL >variables (see the chapter on memory management) although only one bit is really needed to implement this type.

The values used to implement the logical constants .TRUE. and
.FALSE. differ:
          |    VMS     |    Sun    |   IRIX    |    -----------|------------|-----------|-----------|-----------
.TRUE.    |    -1      |     1     |     1     |    -----------|------------|-----------|-----------|-----------
.FALSE.   |     0      |     0     |     0     |    -----------|------------|-----------|-----------|-----------
Unix machines naturally adopted the C convention, VMS has a seemingly strange value for .TRUE., however on a closer look you will see that
if .FALSE. is "all bits 0", .TRUE. should be "all bits 1", in two's complement signed integers the number with all bits set to 1 is -1.

http://www.ibiblio.org/pub/languages/fortran/ch2-3.html

It looks like its for simpler memory management

http://www.ibiblio.org/pub/languages/fortran/ch2-19.html