I want to ask that how can I upgrade the Openssl from 0.9 to 1.0.* in Strawberry Perl version 5.10.*?

Go to openssl.org and download source code or binaries .... until you have a directory with the latest version like this

openssl\bin\libeay32.dll
openssl\exp\libeay32.exp
openssl\lib\libeay32.a
openssl\lib\libeay32.def
openssl\lib\libeay32.lib
openssl\include\openssl\...
[download]

Copy the bin/lib/include that to strawberry perl directory c

...strawberryperl\c\bin\libeay32.dll
...strawberryperl\c\lib\libeay32.a
...strawberryperl\c\lib\libeay32.def
...strawberryperl\c\lib\libeay32.lib
...strawberryperl\c\include\openssl...
[download]

You could try binaries from http://strawberryperl.com/package/kmx/64_libs/gcc49-2016Q4/

After you have appropriate openssl binaries, then

Then install / reinstall any perl modules that depend on openssl, like  cpan Net::SSLeay IO::Socket::SSL

If it works it works, if it doesn't work, then you gotta work through each error .....

A better idea is go to http://strawberryperl.com/releases.html and download a recent PortableZIP edition = suitable for "perl on USB stick" (you can move/rename the perl directory and it will still work)

You can many different portablezip editions installed, as long as you use a different directory for each, they won't trip over each other, and they'll already have a resonably recent version of openssl