These words are often used synonymously but there are some differences worth bearing in mind. First of all, according to http://thesaurus.com/browse/horrendous they go in decreasing degree of horror: horrific, horrendous, horrible, horrid.
Indeed if we check the British National Corpus at http://www.natcorp.ox.ac.uk/ we can see that there are 12 entries for “horrific accident” but only two each for “horrendous accident” and “horrible accident” and none at all for “horrid accident” (although the latter would still be correct). But then that would only work when the meaning was “something that means that it makes us feel horror”. This is certainly how we feel when we see a “horrific accident” but we also have the following usage, taken from http://www.bbc.co.uk/worldservice/learningenglish/grammar/learnit/learnitv154.shtml
horrible: You can describe something as horrible (or dreadful or awful) when you do not like it at all eg. The hotel was horrible – just awful. The walls were all painted a horrible colour and I’ve never had such dreadful meals.
You would not say “horrific” in the context above.
horrific: You would describe something as horrific when it is really upsetting or frightening to think about it or speak about it eg:
Having to survive in the desert for eight days with very little water and practically no shelter from the sun was horrific.
It was a horrific motorway accident: twelve people died, a further twenty four suffered horrendous burns.
You could say horrible in both these examples but “horrific” and “horrendous” makes it sound much more extreme, which is probably more what you want to communicate.
horrendous – horrifying
Horrendous can mean horrifying, describing something you feel dismay or disgust about, but it can also be used in a less extreme way, meaning unpleasant or shocking.
Compare the following:
The traffic this morning was horrendous. It took me seventy-five minutes to travel eleven miles.
It was a horrifying picture: the dead and the wounded had all been left by the roadside.
As for horrid, this is more of an old-fashioned word, often associated with posh, public school types (think Enid Blyton). It can be used just the same as horrific/horrible but frankly always sounds a bit ridiculous to my ears.