What you described here is a limitation in STAAD.Pro that has been there since day 1. One can have as many sets of design as needed however in the postprocessing mode ( GUI ), STAAD.Pro can only display the results for the final design set. The results for ALL design sets would however be output as part of the analysis output file.
This is explained in the following wiki
If you have two serviceability envelopes, each followed by a set of design commands, each set will be designed for the corresponding envelope and independent of each other. The GUI will only display the results from the last design set. If you would want STAAD.Pro to report the most critical of the serviceability cases, you would have include all those cases as part of the LOAD LIST ENV command. For example for your case, if you specify
LOAD LIST ENV 1 2
for a design set, where 1 and 2 are both serviceability envelopes, you will get the more critical of the two reported as the critical condition. In your case you used two separate DFF values for the two envelopes and I think that is the reason you had to use two different design sets and that is OK. Just be aware that these will be deigned independently.
Now coming to the scenario where you are throwing in a STRENGTH envelope into the mix, there are a couple of things to note.
First of all, you cannot have the same load case/combination assigned to both serviceability and strength envelope. If you do, the final assignment would prevail. For example in your case, load 4 would be considered as a strength load case. If you would like to check the same load case for both serviceability and strength, you would have to follow the procedure explained in the wiki below
Secondly you are getting warnings that no deflection check is carried out because your second and third design sets both have load case 4 as the active load case and it is a strength load case for the reason mentioned above. So there is no service case per say for these two design sets and hence the warnings.