What do you call sensations without stimuli? Sometimes, when you close your eyes in the dark, you see what looks like sparks or flashes. Sometimes when you are tired, your vision seems to shift sideways and realign, like someone bumped into a camera, although you didn't move your eyes. It seems to me that some of these apparent sensations are not caused by (external) stimuli to the sensory apparatus but rather by an "overexcited" nervous system.

Is there a term for such "mistakes" of the visual system? I don't know what terms to use to describe these phenomena in scientific reports.
Short answer
Visual hallucinations and, more specifically, phosphenes are the terms you are probably after.

Background
I'll basically provide a list of terminologies below, as your question seems to indicate you're walking on unfamiliar grounds with your research.


For a starters, sensations refer to the peripheral detection of stimuli. Perceptions are the higher cognitive, central correlate of those sensations involving the conscious awareness of them.
The sparks or flashes you're talking about may be caused peripherally (sensation level), but likely find their origins centrally (perceptual). This, because people with low-vision, or blind people lacking functional photoreceptors in their retinae can experience them too, and sometimes in exaggerated and pathological forms.
The visual field shifts are most likely caused by eye movements, unless you can provide solid sources to back up your thoughts that it can happen without eye movements. Likely, nystagmus or related involuntary eye movements are involved, which can be exaggerated by some physical conditions, again including blindness.
Now, as my knowledge is restricted to visual impairments, I can say that spontaneous spots of light are not sensations, but hallucinations. A hallucination being "...a sensory experience, possessing the compelling sense of reality of a true perception, but occurring without external stimulation of the relevant sensory organ. Specifically, they are elementary visual hallucinations, as opposed to complex visual hallucinations. An example of the latter is the Charles Bonnet Syndrome, where blind folks experience complex visual scenes, including faces. 
Back to your question on elementary visual hallucinations, they are referred to as phosphenes, photopsiae, or unformed visual hallucinations, Typically they consist of colored or colorless bright lights, such as points, flashes, stars, and sparks. To provide some context to these terms: Phosphenes are generally used to describe benign phenomena, as well as for stimuli evoked by electrical stimulation of the retina or other visual centers (forget about the latter for the sake of simplicity, as these are not hallucinations anymore). Photospsias are generally used in the literature associated with retinal disease. Unformed hallucinations, personally, I've never encountered in my field of research, but the linked article below gives it as a last option, so I simply included it here too.


Reference
- Menen et al (2003), Survey of Ophthalmology; 48(1): 58–72