Besides Java, what other coding languages are heavily used in the software industry (Especially for companies like Google, Apple, Microsoft, or Facebook).

There are lot of languages used at big companies like C++, Java, Python, Golang, etc.
You don't need to know all of them. Knowing any one object oriented language very well is good enough for getting job. You should be good at coding, algorithm, data structures & CS fundamentals. This is what will help you to become good software developer and get job at big tech companies. To develop coding skills you can look at websites like topcoder & codechef. You should also participate in coding competitions like ACM ICPC at school to develop coding skills.

This depends on what part of the system you're working with. Server end engineers tend to use a lot of Python, Ruby, and PHP. Web engineers also use quite a bit of PHP and Javascript. Mobile and Desktop Java, Objective C, C# and C++. Also new languages such as Go and Swift are starting to gain traction.

Keep in mind though Learning the syntax of a language is easy, the hard part is actually understanding how and why things work as they do. If you have a good understanding of computer fundamentals in C++ or Java or any other language picking up a book and figuring out a different or new language is relatively easy. To really become a great engineer focus more on the fundamentals such as data structures, memory management, system design and architecture, don't worry so much about learning a specific language or syntax that will follow. Keep in mind that languages that are popular today might not be 3-5 years down the road and if syntax is all you know you'll be left behind.

Lots!

SQL, for data
Python
Javascript in the browser and in node.js.
Ruby on Rails
C#
Golang
php

C++ and C when performance is critical and development labor is not.

There are also many frameworks you can use.

Great software engineers know how to use a large number of languages and can pick the right one for each task. Mediocre and bad engineers decide one language is the "correct' one.

Nothing more to add except this link that you might find useful: Technical Development Guide

JavaScript, PHP, C#, Ruby, Python, C++, and Scala are the big ones, aside from Java. Java is a great language to start from because it has origins in C and C++, is an established compiled language, sits on top of a seasoned VM (the JVM), and is a good starting point for other C-based languages like JavaScript and C#.

I agree with what most of the people are saying and that is learning Java is a great start that will help you learn programming in general and object oriented programming in particular. That will get you a long way to be able to learn C++, C#, Groovy, JavaScript, etc. SQL is very important as that is what databases use to get and update information.

But Java first! It's an Object Oriented language and it's used everywhere. Honestly after that I wouldn't so much worry about most used languages, but I'd find one that you enjoy working with. Python and Ruby are probably the next most helpful to know, but find one you like, if you can.

One thing that I don't think was mentioned here is BASH scripting. It's not a technically a programming language but it has commands and syntax and such. It will allow you to do command line scripting. If you do a lot of java you will likely have to call those Java compiled programs called jar files from the command line and BASH scripting knowledge will come in very handy.