If the Sony has an ""export" choice for contacts, export them, preferably in csv format. Then you can import them to your Google account and your phone will pick them up.
If the Sony has some other export format, someone may still be able to "coerce" the data into a form that either Google or your phone can import. (Data conversion is one of the trivial and fun parts of computer programming.)
If not, start toughening up your thumbs. You're going to have to enter them one by one. Put them into Google Contacts - it's easier on a computer than on your phone.