Sensory dissonance: Will the visual or auditory channel win? Is there any research showing that our visual channel takes precedence over the auditory channel (or vice versa) if there is some dissonance between them?
Examples:

Say a person driving a car approaches at fast speed a road split bang in the middle, the person next to her shouts &quot;Right!!!&quot; but raises his arm and clearly pointing to the left.

Being shown the word 'Red' (coloured red) but simultaneously hearing the word 'Blue', will subjects press the red or the blue button?
Yes. The phenomenon is usually referred to as Visual Dominance or Visual Capture.

A very nice demonstration of it, is known as McGurk Effect, in which our vision of the speaker's lips biases our perception of the sound we hear [1]. The McGurk Effect can be seen in a demo video here. Another demonstration of a similar effect is ventriloquism, in which we perceive the sound as coming from somewhere "probable" (like a puppet's vigorously moving lips) and not from its true origin.

One early scientific research into the matter of resolution of conflicting information between senses was done by James Gibson, in a study from early 1930s [2], in which subjects wore prism spectacles, that made straight lines appear curved. Although this was not the main topic of the research, he reports that


  When a visually curved edge such as a meter stick was felt, it was felt as curved. This was true as long as the hand was watched while running up and down the edge. If
  the eyes were closed or turned away, the edge of course felt straight, as it in reality was. This dominance of the visual over the kinsesthetic perception was so complete that when subjects were instructed to make a strong effort to dissociate the two, i.e. to 'feel it straight and see it curved,' it was reported either difficult or impossible to do so.


Posner et al. [3] cite several studies showing visual dominance over proprioceptive, haptic and auditory information, both in perception and in memory judgments, and try to explain the origins of this effect. 

Specifically addressing your question of vision versus audition, Colavita [4] conducted a study in which


  Human Ss matched an auditory and a visual stimulus for subjective magnitude. Then each stimulus was used as a cue in a reaction time task. On occasions when both stimuli were presented simultaneously, Ss’ responding was seen to be dominated by the visual stimulus. Of further interest was the finding that on some occasions of simultaneous light-tone presentation Ss were unaware that the tone had been presented. This apparent prepotency of the visual over the auditory stimulus was seen to persist across a variety of experimental conditions, which included giving Ss verbal instructions to respond to the tone when both stimuli were presented simultaneously.


However, there are also reports of the opposite case, visual information is dominated by other sources, for example by haptic information when vision is blurred [5].

Recently it has been claimed that it integration between senses is done an optimal way, i.e the more accurate source in each situation is given more weight in their combination, or relied upon to a larger extent [6]. Since vision is usually very accurate in terms of location and shape of objects in the world, it tends to be dominant more often then other senses.



References


McGurk, H., &amp; MacDonald, J. (1976). Hearing lips and seeing voices.
Gibson, J. J. (1933). Adaptation, after-effect and contrast in the perception of curved lines. Journal of experimental psychology, 16(1), 1. PDF
Posner, M. I., Nissen, M. J., &amp; Klein, R. M. (1976). Visual dominance: an information-processing account of its origins and significance. Psychological review, 83(2), 157. PDF
Colavita, F. B. (1974). Human sensory dominance. Perception &amp; Psychophysics, 16(2), 409-412.
Heller, M. A. (1983). Haptic dominance in form perception with blurred vision. Perception, 12(5), 607-613. PDF
Ernst, M. O., &amp; Banks, M. S. (2002). Humans integrate visual and haptic information in a statistically optimal fashion. Nature, 415(6870), 429-433.