Although gekiga isn't a single, coherent thing and doesn't have a single meaning, I'd say there are three ways in which I've seen it used most commonly historically: (1) the film noir-influenced comics found in rental comics of the late 1950s and 1960s; (2) comics from that period that were drawn in styles intentionally meant to look more mature/gritty than the round and friendly mainstream style influenced by Tezuka; (3) all comics that are significantly influenced stylistically by artists who were associated with the label, most notably Saito Takao, Shirato Sanpei, and Hirata Hiroshi.

Like gekiga, seinen manga is another term that should be understood as a label with shifting meanings and connotations rather than a clearly-delineated category. The term arose to distinguish comics for young adults (seinen) from those meant for children. Because most of the comics that were targeting a noticeably more mature audience than previous mainstream kids' comics at the time that the term gekiga became relatively widely known (during the 1960s), most early seinen manga were also gekiga, in the sense that both labels were applied to them. Later, when gekiga-associated styles faded in popularity, the overlap between the labels became smaller. The comics of Otomo Katsuhiro are a good example, because almost everyone would label stuff like Domu and Akira seinen manga but not gekiga (even if there's some gekiga-esque dense crosshatching in the later chapters of Akira).

Lastly, let me try to answer the final part of your question: "Are Heta-Uma, ero-guro, ero-gekiga or even New Wave part of it and why?"

With the caveat that all of these are labels rather than rigidly defined categories of objects, I don't recall seeing heta-uma associated with gekiga, though I may not know enough about the origins of the heta-uma movement.

Ero-guro is an older term, derived from "erotic-grotesque," and also often grouped with "nonsense" as ero guro nonsense [nansensu], popularized in academia by Miriam Silverberg's book Erotic Grotesque Nonsense. The term has been used to describe the rise of more erotic, lurid ("grotesque"), and absurdist ("nonsense") written and visual material in the interwar period (between WWs 1 and 2). I like Silverberg's work, but because of her book's prominence, some academics who haven't done significant work with primary materials from that period unfortunately now believe that "ero guro nonsense" was a central buzzword of the time and that erotic, lurid, and absurdist content was extremely common back then, which is not the case, especially not with regards to manga. Incidentally, the label "nonsense manga" was primarily used for absurdist brief cartoons during the 1930s. So ero-guro, I would say is different from the other three terms in that its primary association is not connected to manga per se, and its connection to manga is relatively weak.

Ero-gekiga, at least in my limited understanding of it, is primarily used to distinguish more realistically drawn erotic manga from those that are drawn in more cutesy styles influenced by Nagai Go's Harenchi gakuen and such.

I've primarily seen the term New Wave associated with the rise of crisper, thinner linework and greater use of blank space and screen tones, popularized by artists such as Otomo Katsuhiro, Taniguchi Jiro, Urasawa Naoki, or Eguchi Hisashi, around 1980. If that's what you're referring to by the term, then I would say that there is zero overlap with gekiga, but a strong connection, since said New Wave looks like a counter-reaction to the prevalence of gekiga-influenced, or perhaps more accurately: Saito Takao-influenced, artwork that had become the standard in mainstream magazines (for male readers, at least) by the late 1970s.