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At my job we do this currently fairly easily just by putting each version under it's own application folder in IIS, so we have URIs like:

http://SomeServiceBox/Service/v1.0/
http://SomeServiceBox/Service/v1.1/
http://SomeServiceBox/Service/v2.0/
http://SomeServiceBox/Service/v2.3/

Works just fine for us. I can only suggest this until you explain why you wouldn't already be doing such... I'm guessing there's something in the way your service is put together that makes such an approach non-functioning otherwise you would have already done this.

If you are making a standard web app, then TLS is your only "safe" method of protecting users from MitM attacks and traffic sniffing. Take a look at ipviking's map of real time cyber attacks; a large number come from China because encryption is largely outlawed and browser requests can get hijacked. (Most infosec guys I know agree that X.509 is broken, the IETF is compromised, TLS is likely weakened intentionally by the NSA (kinda like this), and the entire key spaces for RSA and elliptic curves are being precomputed by governments. Nevertheless, it is still better than unencrypted traffic.)

If you must use security questions, I suggest putting everything in lowercase, stripping out whitespace, and hashing with a random salt stored along side it (it could be a single salt stored as part of a user record). I suggest at least 256 bit hash and 100 rounds (fewer if hash algorithm is already slow). Bcrypt hashes are also quite good because they involve encrypting a hash and storing the salt as part of the hash string.

If not using bcrypt, then be sure to not use a simple str1==str2 boolean for checking the answer; you should use something like the following, which will avoid the string comparison side channel attack.

function compHashes ($h1, $h2) {
    $r = 0;
    if (strlen($h1) !== strlen($h2)) return false;
    for ($i=0; $i<strlen($h1); ++$i)
        $r |= ord($h1[$i])^ord($h2[$i]);
    return $r == 0;
}

The considerations for binary apps are a little different in that you can hard code or bundle a public key (or several) and use NaCl to generate client private keys and handle handshakes and encryption between server and client. There are libraries in every compilable language for this, and writing a wrapper for a statically linked library is not too difficult if that is the route you choose. Rolling your own crypto is definitely not recommended if you are not very familiar with cryptography and infosec matters.