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I have a conceptual model with 3 regular independent variables and one dependent variable. Next to those three independent variables, I have another moderator variable possible affecting the relationship of two out of three regular independent virables. This makes it actually four independent variables.

I am currently running a three-way anova test with the three regular independent variables. However, I am not sure how to investigate the potential role of the moderator. Actually, I am not sure if I am approaching it in the right way at all.

Below a screenshot of my conceptual model is attachedenter image description here

Review Extremety, Review Breadth and Identity Disclosure are dummy variables (I did an experiment). Product involvement is a continuous variable. Does anyone know what would be a good way to investigate this? Thanks in advance!

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Your diagram pretty much answers your question, once you recognize that (1) a moderator is represented as an interaction term in a regression model and (2) you should include a term for the moderator itself besides the interaction term. Don't worry about whether this ends up being called a "three-way ANOVA" or whatever. If you construct the regression according to your model, the result will represent what you intend to test regardless of what you call it.

If Perceived Review Helpfulness is a continuous outcome then you have a multiple linear regression. All the various types of ANOVA, ANCOVA, etc. can be represented as multiple linear regressions; software typically fits them all with multiple regression methods. You would include Review Extremity, Review Length, Identity Disclosure and Product Involvement as predictors, and add interactions of Product Involvement with each of Review Length and Identity Disclosure. That gives you 6 terms (besides the intercept) in your model. If you have on the order of 60 to 120 cases, you should be able to fit your model without too much risk of overfitting.

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