In general, strains and species are more closely related to each other (shared a common ancestor more recently) while genus, family, class etc are less related to each other (shared a common ancestor longer ago), but different organism types have been classified by humans differently, so different isolates of the same "species" of retrovirus for example are thousands of time more diverse than different Genera of mammals for example. Even within bacteria, humans treat some types differently than others, with the enterobacteria for example being divided more finely than the Clostridia. When you say "pathogenic organism" you might be speaking of virus, bacteria, protist, etc and there is no way to really know what level of diversity you are speaking of. Even within the world of HIV-1 M group viruses (one "species" with a lot of diversity) we can study evolution and recombination at many levels such as within a single patient over time or between isolates of the same subtype in one country or between subtypes that have evolved in different parts of the world and have now come back together because of boats and jet airliners.

In general, strains and species are more closely related to each other (shared a common ancestor more recently) while genus, family, class etc are less related to each other (shared a common ancestor longer ago), but different organism types have been classified by humans differently, so different isolates of the same "species" of retrovirus for example are thousands of time more diverse than different Genera of mammals for example. Even within bacteria, humans treat some types differently than others, with the enterobacteria for example being divided more finely than the Clostridia. When you say "pathogenic organism" you might be speaking of virus, bacteria, protist, etc and there is no way to really know what level of diversity you are speaking of. Even within the world of HIV-1 M group viruses (one "species" with a lot of diversity) we can study evolution and recombination at many levels such as within a single patient over time or between isolates of the same subtype in one country or between subtypes that have evolved in different parts of the world and have now come back together because of boats and jet airliners.

I agree with Brian Thomas Foley above that the choice of strains from same/different species/genera eventually will reject the divergence level.

The power of your analyses for selection and recombination will be affected by divergence as it defines how much information you have in your data. If your sequences are too diverse, or if your sequences are too close then you ar unlikely to find a signal (low power). There are many publications by now that have shown this, including some from my own: Anisimova et all 2001, 2002, 2003 and Anisimova and Yang 2007.

So divergence is one factor. Another factor to consider is what type of sampling you have and how well it corresponds to your actual question. Do you have mixed population and species data? Are you interested in lineage-specific effects? Are you interested in detecting episodic selection. Are you contrasting your sets of strains by some criteria (e.g., pathogeneicity or environment, etc.)? Basically, you can analyse any sample set, but the success of your analysis will depend on what specifically questions you are asking and whether your sample is the best one to provide information to answer these questions. So there you have to be careful what tests to set up and how to interpret them. I don't know if this helps, but I don't know specifically your scenario.

The ability to detect the signature of positive selection and recombination depends on the level of nucleotide diversity (pi) in the data (see Maria Anisimova's answere above). There is an optimum level of pi that will give you the best chance (most statistical power) to observe evidence of these evolutionary forces. Depending on the phylogeny, this optimum level might be at the level of ecotypes, species or genera (or even at higher-level taxa comparisons). David Posada and Keith Crandall did an excellent study on this, evaluating the power of different recombination methods ( Posada, D., & Crandall, K. A. (2001). Evaluation of methods for detecting recombination from DNA sequences: computer simulations. Proceedings of the National Academy of Sciences, 98, 13757-13762).

Furthermore, although the signal of recombination is often best observed in areas with high levels of polymorphism (e.g. Jouet et al 2015 Mol. Ecol. 24, 3077–3092), this may be due to an observer bias. "Too much" recombination homogenizes the nucleotide variation across your sequences, thus wiping out its own signature. (Too much footprints in the snow). For that reason, you may want to compare the coalescence times across the multiple genomes. When doing this, you would ideally analyse polymorphisms at 3rd codon position to avoid confusing the homogenising effects of recombination with purifying selection acting on polymorphisms in most 1st and 2nd codon positions. We developed software to do this very rapidly across multiple genomes (https://github.com/Ward9250/SpeedDate.jl). If you find areas with unusually low divergence times, this may be caused by recent introgression across your sequences, although other processes such as selective sweeps can also be responsible. Hence, doing the recombination analysis across different levels of the taxonomy (species as well as genus levl) is a good idea.