Fear. Politics. Fear. Closer to Home. The Chosen One. Psychology.
No other country wanted to try and help through fear if Voldemort won then who would be next? The country that helped the people standing in his way.
You have to remember that the British Ministry of Magic fell. That would insightinstill fear into the Ministry of Magic equivalents in other countries. Also the wizarding worlds don't really have armies, the Ministry has Aurors, up until The Battle Of Hogwarts only the Order of The Phoenix stood in Voldemort's way and only a few members were known openly. (It can be argued all good teachers were also members of the OOTP however not openly)
Yet more fear, Dumbledore was known to be the most powerful wizard of the time although I would say the general consensus was torn between him and Voldemort. When Dumbledore died I would imagine this would strike fear into the hearts of anyone who had ever met him.
The question about international wizards arises a lot but when you think about it how many English wizards actually helped out in the fight against Voldemort? Not many at all, people hid from him and from his pure blood regime but most did not fight. Only the Aurors and the Order fought.
England also had what the media had dubbed "The Chosen One" he would no doubt save the day. The hope of the free world was resting upon Harry's shoulders and if he couldn't do it who could?
Also the Bystander Effect: it is a lot easier to stand by and do nothing if everyone else around you is standing by and doing nothing. More keywords include Diffusion of Responsibility the more people are witnessing the less the responsibility you feel to actually do something. So for all the countries standing by they could all say well "no one else is helping out why should we". Interesting to read up on would recommend.