Well, many philosophers far more advanced than I have devoted whole books to this subject, but I'll try for you, Pipirr.
It's true, that defining post-modernism is contentious and difficult. Indeed, most of the philosophers most strongly identified with post-modern thought, such as Michael Foucault, did not self-identify as post-modern. However, let me try and explain my use of the term, which might help refute this misconception that postmodernism somehow implies "everything is equally true", which is certainly not the case.
Personally, I equate the term "post-modernism" most strongly with "post-structuralism", and it seems to be a misreading of post-structural thought which has lead to the image of post-modern thought such as the OP.
The
Wiki entry on Post-Structuralism quotes Derrida, stating that "it rejects definitions that claim to have discovered absolute 'truths' or facts about the world". Whilst this might, at first glance, seem to imply that anything goes, or that post-structuralist thought inherently rejects scientific empiricism. However, the post-structuralist arguments are far more nuanced than this, and essentially seek to refute the central claim of
Structuralism that rejects "the concept of human freedom and choice and focused instead on the way that human behavior is determined by various structures".
The truth that postmodernism criticises, then, is what might be shown to be constructed truth - that is, the truth of the meaning of a painting, or the truth of the rigid gendering of certain biological tropes. Post-structuralists argue that what makes a boy "a boy" is not inherent but constructed by culture and society, and they argue that meanings of art works are personal to the reader, not imposed by the artist.
It makes no claim on empiricism, per se, and tends to refer to things beyond the empirical reach of science, as Matt the Poet pointed out earlier on.