She's clearly bonkers...[spoilers]
...or the film makers want us to believe so.
A few things at the very beginning tip us off. Her prayer or speech that precedes the interview contains a quote taken from the uncle. Then, her first words once the movie proper start are "Yes, I have an imagination!" or words to that effect.
She reveals that if she accepts, this would be her first post as a governess. Finally, her first days at the estate reveal that she is a nervous hypersensitive who sleeps poorly.
So, we see within the first 20 minutes of the film that Ms. Giddens is easily influenced, highly imaginative, lacks practical experience in the greater world (or of children's behavior), and is a bit neurotic, as well as being the expected uptight, repressed Victorian-era babe she is.
But then we see and hear a few film-making devices that cement the idea that Giddens is responsible for all that occurs:
1. Her first act upon entering the house is to gently touch some flowers, causing them to fall apart. This shows her innate capacity for corruption.
2. Upon entering the tower ground floor, we hear the buzzing of flies. Her thoughts regarding Miles are already suspicious, due to his expulsion; she externalizes this by "seeing" and pursuing the man in the tower.
3. After seeing Quint at the window, Giddens exits through the window, then returns, peering through the glass just as Quint had. This unnecessary behavior reveals Giddens is subconsciously projecting herself onto a phantom.
4. After setting down and lovingly caressing her bible, an errant flower petal falls to its cover. Her goodness and desire to help, learned by her father, a pastor, is negated by her innate capacity for corruption through suspicion.
5. As Giddens enters the schoolroom just prior to seeing Jessel, we hear the buzzing of flies. It stops as Giddens sees Jessel. After discovering the "tear" on the desk, the buzzing resumes. It is at this point that she decides that the children are possessed, i.e., her delusion is nearing it's peak.
6. Once Giddens is told that Jessel killed herself, Giddens wears a black dress from then on to the ending of the film. Once again, she projects herself onto a phantom. Giddens was told that Jessel went into deep mourning following Quint's death, then shortly thereafter died herself, but it is only after being told that it was by suicide - truly shocking - that Giddens assumes this behavior.
These points demonstrate both Gidden's capacity for corruption/destruction and her capacity to project herself into the "roles" of both Quint and Jessup, by mimicking (what she imagines is) their actions and dress.
We know Giddens was capable of these behaviors/delusions well before she arrived at the house, so the influence of "ghosts" is highly unlikely.
Were the children influenced by Quint and Jessel? Yes, almost certainly, but only while those people were still alive. Giddens has a can of worms for a mind and it is she that is responsible for all that occurs in the film, up to and including the derangement/death of the children.
"...if only you could see what I've seen with your eyes!" Roy Batty