When to use standard versus moderator regression techniques for the most parsimonious approach? I know how to run multiple regressions (SMR, HMR, and MMR) in SPSS but I'm still a little vague on when it's appropriate to use each of them to achieve the best and most parsimonious result. (SPSS being the mathematical software, SMR being standard multiple regression, HMR being hierarchical multiple regression, and MMR being moderated multiple regression, SMR and SPSS are further explained in this video, hierarchical multiple regression in this video, and moderated multiple regression in this blog post). 

e.g. in a case where I want to see the impact of social anxiety, and sense of humour on life satisfaction, I hypothesise that both social anxiety and sense of humour will be individually associated with life satisfaction.

When controlling for age, gender and anxiety, participants high in sense of humour will have higher life satisfaction. 

Also, when excluding variables of age and gender, I predict that the negative association between anxiety and life satisfaction will be stronger for those with low sense of humour ratings. 

I feel that for most of these questions, the answers could be found using an SMR, and the last question, with an MMR, but is there a simpler and more parsimonious way to do this? Can I gather the data for the first few questions from the MMR analysis, for example?
You write: 


  When controlling for age, gender and anxiety, participants high in sense of humour will have higher life satisfaction.


This is standard regression. Predictors that are control variables are the same as any other predictors, it's just that their inclusion in the model is mostly there to facilitate a desired interpretation of a focal predictor.


  Also, when excluding variables of age and gender, I predict that the negative association between anxiety and life satisfaction will be stronger for those with low sense of humour ratings.


Here you have described a moderation hypothesis.
i.e., in regression terms, you might express it like this:

lifesat ~ anxiety * humour


However, technically, you have not assigned anxiety or life satisfaction a particular status as the outcome variable. Whether you "exclude age and gender" is irrelevant to the status of the hypothesis as a moderation hypothesis.

You ask specifically:


  I feel that for most of these questions, the answers could be found using an SMR, and the last question, with an MMR, but is there a simpler and more parsimonious way to do this? Can I gather the data for the first few questions from the MMR analysis, for example?


Don't be afraid to run several regression models. Ultimately, a moderator regression is simply a model with an interaction term. Adding predictors generally alters the regression coefficients for other predictors (an exception would be for orthogonal variables, such as in experiments).