Your code probably looks like this:
class OAuthSignatureMethod_HMAC_SHA1 {
...
}
It should look like this:
if( ! class_exists( 'OAuthSignatureMethod_HMAC_SHA1' ) ) :
class OAuthSignatureMethod_HMAC_SHA1 {
...
}
endif;
This is more a PHP issue than a WordPress issue, but if multiple plug-ins include or require files that declare the same class with the same name, you’ll get a collision. You only need to define the class once, then you can instantiate it as many times as you need in your multiple systems.