Yes, nominal predictors can be employed in even standard regression models.
Now, as you asked the question: "I would like to know which one of predictors have more influence on the predicted variable", I would simply recommend that you focus on 'Standardized Beta Coefficients'.
The standardized coefficients are computed by centering the data (subtracting means) and scaling by the respective standard deviations in the regression model. Per the cited source:
A standardized beta coefficient compares the strength of the effect of each individual independent variable to the dependent variable. The higher the absolute value of the beta coefficient, the stronger the effect... This means the variables can be easily compared to each other. In other words, standardized beta coefficients are the coefficients that you would get if the variables in the regression were all converted to z-scores before running the analysis.
And also, of import as the unstandardized dummy variables can have different standard deviations:
In regression analysis, different units and different scales are often used. For example, one variable might use dollars and another might use percentages. Standardizing coefficients means that you can compare the relative importance of each coefficient in a regression model.
The corresponding t-tests indicates the significance levels of the respective standardized beta coefficient.