I have three variables,
1. Irrational Beliefs (Categorical)
2. Anxiety State/ Trait (Categorical)
3. Personality Traits (Categorical)
Which statistical analyses can be used?
@onestop is literally correct. If you have three unordered categorical variables, techniques like loglinear modelling are appropriate.
@Neelam However, I doubt that your data is unordered categorical.
From my experience with measures of psychological scales measuring irrational beliefs, anxiety states and traits, and personality traits, the scales are numeric.
For example, a typical personality scale might have 10 items with each item measured on a 5-point scale. Thus, if you were to sum the scale you get scores ranging from a minimum possible score of 10 to a maximum possible score of 50. I.e., there are 41 possible values. Thus, in some sense the variables are categorical, but they are also ordinal, and they are also typically treated as numeric variables. See my comments to this earlier question regarding discrete and continuous variables.
Thus, in the empirical research that I read with similar scales, researchers typically treat such scales as numeric variables. Thus, methods such as correlation, regression, and PCA are standard.