tenere - is basic "hold", hold something in hands ... Correct?
Yes, and also "mantenere". You can tenere something in your hands, in your mind, under your eyes. When driving a car you have to "tenere la destra" in Italy (stay on the right side of the road). Less correctly (dialectal) some people also use "tenere" to mean "to have": "tenere fame" = "avere fame". In some circumstances "tenere" (but not mantenere) means also "resist an effort": "la colla tiene" means "the glue resists". It is a broad verb, there are many locutions using it but it would take lot of space (and memory).
sostenere ... more like support ... not necessary phisically. Correct?
Yes again. In a physical context, to impede that something falls down. In a figurative context it means "to mantain an opinion", "to have and express an opinion", or to approve and support the thought of someone else: "ti sostengo" = "I think the same (and I am supporting you)".
reggere - "hold on", "get over". I must hold on. I must get over this. Is that correct?
Sorry, not quite, especially not "get over": the verb expresses a static situation. It is, physically, very like "sostenere": to avoid that something falls down. Figuratively it is similar, with a few meanings; for example "reggere allo sforzo" = "to withstand the (opposing) force"; in a few cases it means "be in charge" of something quite important, to be the chief, like "reggere il trono" - literally "to keep the throne" (be the king).
To keep it simple, it is mostly the same as "reggere". Perhaps, sometimes one says "sorretto" (past participle) instead of "retto" because this last word can have other meanings.