I see no reason for you to not use the standard ES measures for ANOVAs: https://www.uccs.edu/lbecker/glm_effectsize.html

Thanks for your reply Jan! Would you say I should compute the standard ES measures on the trimmed data, or on the complete data set...? Thanks!

Depends a bit on the data you have. If the outliers you have removed are likely to represent measurement error, then the trimmed data will probably be more generalisable. If the outliers can represent true values (but uncommon values), then I would use the complete data (but then also use the complete data in the ANOVA).

Thanks for your response Jan! Much appreciated. 

 Are you looking for an overall effect size for the ANOVA or for the group/condition comparisons? I mean, the overall effect size is less informative, since it does not capture the single components. I would break it down to the simple comparisons and here you have some approaches, also in Wilcox' books, e.g. functions yuend, yuendv2, D.akp.effect for independent groups and rmmcp for repeated measures. But also have a look at the references.

http://journals.sagepub.com/doi/abs/10.1177/0013164404268675

http://www.apa.org/pubs/books/4316151.aspx

http://journals.sagepub.com/doi/abs/10.1177/0013164406288161

http://psycnet.apa.org/record/2005-12213-004

Thanks for your reply Rainer, much appreciated. That's what I gathered from Wilcox' book as well. I used some of the functions you mentioned for my main effects. I wasn't entirely sure what to do for the interaction effects; I suppose you would have to break it down into the single comparisons as you suggest? For example if I have one between-subjects factor with two levels, measured pre and post, I would have to look at the pre/post comparison for each factor level separately?

What I've opted for now is to report the usual standardised effect measures using the untrimmed data (partial eta squared), but also for the individual comparisons I report the trimmed mean difference as I think this gives the reader a good idea of the magnitude of the effect. 

The choice of parameters always depends on your research question AND what information you want to transport to the reader. My personal opinion is that overall effect sizes do not tell so much about the underlying effects itself. Maybe for broader questions or meta-analyses it is important to report overall effect sizes (as you did), but the questions of interest are almost always in more specific comparisons. Ask yourself, would you be satisfied if I would caculate the ANOVA for you and just tell you: "there was a significant two-way interaction with a partial eta^2 of .19". Or would you ask: "and which groups/conditions differ?"

Maybe this depends on the research field, but I would ask this question. And to answer your question more specifically: in your example I would look at the pre/post comparison at each factor. BUT, maybe this is not of interest for your research question. It could also just be of interest the comparison of the two groups at the post measure (e.g. do they differ after treatment). You do not have to calculate every possible combination of groups/conditions (in a three way interaction, this may be plenty), but only those of interest of course.