As it stands, I think the question is a bit misguided or unclear. The various extant IE languages are mostly similar because they historically derived from a language spoken thousands of years ago. In that respect, the similarity is like the similarity between British, American, Australian and Indian English – they have a common origin. Another reason why languages could be similar is because one language was influenced by another (thus the many Latin-derived words of English are due to the influence of French and Latin, predominantly).
If you want 4 languages with lots of similarity, you could pick e.g. Slavic. Or you could pick Romance. Or Germanic. This is because each of these groups of languages derives from a more recent common language (in the case of Romance, somewhere in the past 1500 years). However, if you want your languages to come from distinct branches of Indo-European, then the task is vastly harder, unless you rely on ancient languages. English is not very similar at all to Hindi in terms of grammar, but Old English is more similar to Sanskrit – structural differences have accumulated over the millenia.
Technically, you can discern similarities between case marking in Icelandic and Russian, but they are sufficiently different to the eye that doesn't know the history of Indo-European that you can't establish meaningful "similarity".
Nothing of significance can be derived from a similarity between two or more languages: significance only comes from including a causal explanation – X and Y are similar because one language borrowed from another; or because they derive from a common historical source; or they are based on a shared fact of human cognition (for example, onomatopoeia); or it is just a coincidence. Most languages that have case inflection have trivial similarity: it is accomplished with suffixes. This is because most morphology is suffixing, rather than prefixing (or other rare types).
The existence of certain phonological processes that are common to IE languages is mostly explained by the fact that certain things are phonetically natural and likely to be "discovered". If you were looking for examples that illustrate "common source" similarities, you shouldn't look at nasal place-assimilation, post-nasal voicing or final devoicing, because these are extremely common processes across languages and reveal more about the nature of humans and language. The similarity between the inflectional morphology of Sanskrit, Greek, Latin, Old Church Slavic is, on the other hand, explained by the fact that the morphemes derive from a common historical source.
If you want similarities that have to do with "the nature of humans", you need to look at maximally unrelated languages, like Chinese, English, Lushootseed, Malay.
If you only look at IE languages, the implication is that you're looking for similarities that are due to historical unity. Assuming that the goal is to exemplify common-original similarities using grammar, that is a very tough bill to fill, using IE languages, because the modern languages are not very similar in grammar. You could maybe gain some traction looking at verb inflection in Slavic, Romance, Icelandic and Modern Greek.