How to study the effects of alcohol consumption on happiness & cognitive function?

I want to study if there's a relationship between alcohol consumption and happiness + cognitive function.

Most of my data is nominal or ordinal.

To measure alcohol consumption:
  • How often respondent has had an alcoholic drink during the last 12 months
To measure happiness:
  • Overall, how satisfied are you with your life nowadays?
  • Whether was happy much of the time during past week
  • Psychiatric Problems has: depression
To measure cognitive function:
  • Computed score from maths questions
  • Computed score from literacy questions

Since I mostly have nominal data (except for the first question to measure happiness, which provides ordinal data), should I stick to Chi square tests and run one for each happiness & cognitive function variable?

I don't think I can go for regression/one-way ANOVA since none of my variables is continuous.

What's the best way to go about it? Thanks in advance!