Buddhism inherently explains there are good (skilful) & bad (unksilful) actions.
The view there are no good & bad actions is called 'nihilism' (natthikavāda) in Buddhism. About 'nihilists' who believe there are no good or bad actions, Buddhism literally says:
Regardless, that individual is still criticized by sensible people in the present life as being an immoral individual of wrong view, a nihilist. For they are criticized by sensible people in the present life, and
when their body breaks up, after death, they will reappear in a place
of loss, a bad place, the underworld, hell.
MN 60
And what is wrong view? 'There is nothing given, nothing offered,
nothing sacrificed. There is no fruit or result of good or bad
actions. There is no this world, no other world, no mother, no father,
no instantly arisen beings [manifest/afffected by instant kamma] ...
MN 117
He holds wrong view and has an incorrect perspective thus: ‘There is nothing given, nothing sacrificed, nothing offered; there is no fruit or result of good and bad actions; there is no this world, no other world; there is no mother, no father; there are no beings spontaneously arisen; there are in the world no ascetics and brahmins of right conduct and right practice who, having realized this world and the other world for themselves by direct knowledge, make them known to others.’ One possessing these ten qualities is deposited in hell as if brought there.
AN 10.211
In Buddhism, good actions cause a reward and bad actions cause a punishment. The scriptures say:
When my concentrated mind was thus purified, bright, unblemished, rid of imperfection, malleable, wieldy, steady, and attained to imperturbability, I directed it to knowledge of the passing away and reappearance of beings. With the divine eye, which is purified and surpasses the human, I saw beings passing away and reappearing, inferior and superior, fair and ugly, fortunate and unfortunate. I understood how beings pass on according to their actions thus: ‘These worthy beings who were ill conducted in body, speech, and mind, revilers of noble ones, wrong in their views, giving effect to wrong view in their actions, on the dissolution of the body, after death, have reappeared in a state of deprivation, in a bad destination, in perdition, even in hell; but these worthy beings who were well conducted in body, speech, and mind, not revilers of noble ones, right in their views, giving effect to right view in their actions, on the dissolution of the body, after death, have reappeared in a good destination, even in the heavenly world.’ Thus with the divine eye, which is purified and surpasses the human, I saw beings passing away and reappearing, inferior and superior, fair and ugly, fortunate and unfortunate, and I understood how beings pass on according to their actions.
MN 4
MN 130 in particuar describes in graphic detail the multitudes of punishments that can occur to those who "didn’t do good by way of body, speech, and mind", such as:
'My good man, didn't you see among human beings kings — catching a
thief, a criminal — having him tortured in many ways: flogging him
with whips, beating him with canes, beating him with clubs; cutting
off his hands, cutting off his feet, cut off his hands & feet; cutting
off his ears, cutting off his nose, cutting off his ears & nose;
subjecting him to the 'porridge pot,' the 'polished-shell shave,' the
'Rāhu's mouth,' the 'flaming garland,' the 'blazing hand,' the
'grass-duty (ascetic),' the 'bark-dress (ascetic),' the 'burning
antelope,' the 'meat hooks,' the 'coin-gouging,' the 'lye pickling,'
the 'pivot on a stake,' the 'rolled-up bed'; having him splashed with
boiling oil, devoured by dogs, impaled alive on a stake; cutting off
his head with a sword?'
Based on the information in the question, the impression is the ideas of Nietzsche are not related to objective morality but instead related to worldly political gains (advantages) & losses (disadvantages).
In Buddhism, objective morality follows the 'Golden Rule' (refer to SN 55.7) and is about not harming oneself and not harming others. Particularly, the reality of harming oneself can only be truly comprehended in deep meditation (where the neurological impacts of bad wicked evil thoughts & emotions can be directly felt by the body). People who minds are affected by the five hindrances and particuarly by drugs & alcohol cannot comprehend objective morality. DN 31 says:
There are, young householder, these six evil consequences in indulging
in intoxicants which cause infatuation and heedlessness:
(i) loss of wealth,
(ii) increase of quarrels,
(iii) susceptibility to disease,
(iv) earning an evil reputation,
(v) shameless exposure of body,
(vi) weakening of intellect (paññāya dubbalikaraṇītveva).
In summary, the purported Nietzsche idea "the strong always oppress the weak" is worldly and unrelated to the objective moralities of true religion and Buddhism. In true religion and Buddhism, the purpose of morality is to prevent disturbing mental states from afflicting the mind; and also to prevent social dysfunction.