Complicated formula for nested ifs based on multiple conditions

I am trying to develop a formula for use in a Google Sheet. We have about 20 categories of customer complaints. We've connected each of these customer complaints to different sections of our internal standard evaluation, which are all scored 1-3. Internal QA performs an evaluation to a Google Form, and I need a formula that analyzes the evaluation according to the following pseudo-code

If(tag1)
    Check(vlookup(eval_ID, eval_range, category A col_index#,0)<3)
        if true, return "Valid"
        if false, continue
    Check(vlookup(eval_ID, eval_range, category B col_index#,0)<3)
        if true, return "Valid"
        if false, continue
    Check(vlookup(eval_ID, eval_range, category A col_index#,0)<3)
        if true, return "Valid"
        if false, return "invalid"
If(tag2)
    Check(vlookup(eval_ID, eval_range, category X col_index#,0)<3)         
        if true, return "Valid"
        if false, continue
    Check(vlookup(eval_ID, eval_range, category Y col_index#,0)<3)         
        if true, return "Valid"
        if false, return "invalid"
If(tag3)
    ...

Each tag has different categories, and different numbers of categories. Does anyone have a suggestion for how to write this formula? I don't want to use VBA because I want it to automatically calculate as the form is populated rather than manually running the macro.

I'm not sure where to start. Any advice is appreciated, thanks in advance!