How to play Heroes of Might and Magic 2 on Windows 7?

There's no specific emulator for the HOMM series, from what I can tell. Most people are using DOSBox, and if you have access to the DOS edition of the game, it's worth setting up and using. There are many older games that run under DOSBox, and it's pretty easy to set up and maintain compared to a virtual machine or similar solution. DOSBox rates this game as "playable" and you can use the user reports on that page to avoid any common errors and understand what might not work properly.

If you have the Professional, Ultimate, or Enterprise editions of Windows 7, Microsoft Support suggests using Windows XP mode to run HOMM2. This is pretty similar to your VirtualBox solution, but if you've got it built into the OS, you might as well use this as a shortcut.

Sometimes editing the compatibility settings of an application can get it to run in newer Windows versions than the one it was designed for, but given that the game is so old, it's unlikely to work. Given its low time/effort investment, its still worth a shot, though.

To bypass the invalid 16 bit application error

1) Put the disk in and "explore/open" the disk content. Find the folder called "HEROES2".

2) Copy that entire folder to the C:/ drive or wherever you want it.

3) Look inside the copied "HEROES2" folder - it will have a folder called "WING". Open that folder and and copy the .dll contained within it.

4) For 32bit - Copy that .dll and paste it in system32. For 64bit - Copy that .dll and paste it in system32 AND sysWOW64.

5) Go back to the "HEROES2" folder and pin the .exe that has the image and not the white application box to taskbar or create a shortcut.

Heroes 2 should now load when double clicked on without ever using the installer.

As long as you have the original game data (HEROES2.AGG and map files), you could use the free heroes 2 engine (fheroes2), which is Free Software (GPLv2 licensed), developed using SDL (Simple DirectMedia Layer) and as such is compatible with most operating systems. There's even a port for Android!

It's not technically an "emulator", since it adds some extra features and doesn't focus on being a 100% exact clone of the original game engine. The AI leaves something to be desired but other than that it is a pretty good project with an active community of developers.

I haven't tried running the original game on a Windows 98 virtual machine, but that's probably the best way to get 100% compatibility with the original game engine.