I think by "event" people typically mean a change. Biochemical reactions (including the various steps of splicing) are rarely 100% but rather in some form of equilibrium, and the conditions determine where that equilibrium lies. So every cell where a gene is expressed likely has multiple isoforms of the transcript, and their ratios are determined by the conditions. So looking at PSI levels by themselves without comparison is not necessarily very meaningful. I assume you have some kind of controls (untreated/wild-type), so you can compare each of your genotype/treatment groups to a control and make a statements like "applying treatment X results in n events" for each treatment/genotype (and you can plot those numbers in a bar graph, or whatever; typically the events are split by type, like SE, RI, etc., so you can see if a treatment favors one event type over others). For that you need to define "event", and that is at the minimum a cutoff (like 0.05) applied to the p-value (adjusted for multiple testing, FDR), ideally combined with some kind of biological significance threshold involving the ∆PSI (either the absolute value or relative to e.g. the level in the control). Since this is an overview, you can't really fine-tune this cutoff to the specifics of the biology, so just pick something that weeds out most of the spurious stuff without throwing the baby out with the bath water.
If you really want to use the PSIs for each sample directly, you could try to correlate the samples based on PSI values for each gene. (Not sure how best to handle genes that are not expressed in some samples -- maybe throw them out.) Then you can create correlation heatmaps or dendrograms showing how closely the samples are related. You could also try principal components analysis (PCA; plot two or three dimensions) and see if certain groups cluster together. I have never tried this, and given how noisy the PSI values seem to be (possibly a result of expression, see below), I am not sure if you'll get much out of it, but it's easy to try. (If you do it, let me know.)
You were worried about the high variation among samples of the same group. If you use the comparison approach, where you get (adjusted) p-values, that should take care of the variation -- if it is too high, the difference is not going to be significant and it's a "non-event". Note that PSI by itself also does not mean much -- if the gene expression is very low, a difference of 1 count can change the PSI a lot.
Hope this helps you think about it.