Could someone please sort the level of each of these verbs in the degree of horror?
appal, dismay, horrify, shock, startle
From least to worst, I would say:
This implies a small, sudden, shock - something which is quickly dismissed because there was no actual peril.
I was in two minds whether to put this first or second. It means to be concerned about something, so as this implies a genuine cause for that feeling I feel it is "worse" than simply being startled. However, in common usage "dismay" does not really carry the idea of a sudden or unexpected event (even though dictionary definitions say so) and many speakers use it to describe feelings about an ongoing or prolonged issue.
A shock can also turn out to be something benign - just something sudden that takes you by surprise. When used for something ongoing (eg. This situation is shocking!) this plays down the surprise element somewhat. Still, this is worse than a "startle".
The dictionary says this is something that "fills you with horror". Overuse of words does subtract from their impact somewhat, and while the term "horrify" is more widely used than "appal", the word "appalling" is used more than "horrifying". For this reason I was also in two minds about these final two rankings.
As mentioned above, "appalling" is widely used, and while the dictionary defines it as "greatly horrified" it has to rank above "horrify" which would rank it as worse, I am not completely sure that it ought to be. "Appalling", to me, is more about feeling disgusted than scared. People say that food or service is "appalling", whereas the word "horror" is far more synonymous with fear. So, I've ranked it here as the dictionary says I should, but I would consider taking it off this list alltogether (along with "dismay") if you are strictly talking about levels of fear.