Is carbon and oxygen ionic or covalent?

Carbon is a metalloid

ie

element having properties neither as a pure metal nor as a pure non metal. Ionic or electrovalent

bonds are formed by elements with valency less than 3 or 5-7. So carbon forms covalent bonds satisfying its need for 4 more electrons. As an example take a molecule of methane that is CH4. C has electronic configuration :-2 4 ,so to complete its octet it needs 4 electrons more. This is achieved by sharing 4 electrons of hydrogen by overlapping with its orbitals. This sharing of valence pair of electrons results in the formation of a covalent bond.

Under certain circumstances but rarely, carbon will form ionic bonds as a carbide.

CaC

2 exists as does Al4C3