oily

ˈɔɪli

Oily describes both physical properties (substances, skin, or hair coated in or resembling oil) and an unpleasantly smooth, ingratiating manner in a person. The right German equivalent shifts considerably depending on whether the literal or figurative sense is intended.

1. fettig

The most common equivalent for things covered in or containing grease or fat, especially skin, hair, and food.

She has naturally oily skin and uses a mattifying moisturizer.
Sie hat von Natur aus fettige Haut und nutzt eine mattierende Feuchtigkeitscreme.

The takeaway left an oily residue on the paper bag.
Das Takeaway hinterließ einen fettigen Rückstand auf der Papiertüte.

2. ölig

Used when oil itself is the substance in question: oily liquids, contaminated water, or mechanical contexts.

After draining the engine, the workshop floor was streaked with oily marks.
Nach dem Ablassen des Öls war der Werkstattboden mit öligen Schlieren bedeckt.

An oily film spread across the surface of the harbour.
Ein öliger Film breitete sich über die Hafenoberfläche aus.

3. schleimig [informal] · figurative

For people who are unpleasantly ingratiating or sycophantic: the colloquial German equivalent for the figurative sense of being too smooth and insincere.

Nobody in the office trusted his oily charm.
Niemand im Büro traute seinem schleimigen Charme.

He gave an oily smile and assured everyone the deal was perfectly safe.
Er lächelte schleimig und versicherte allen, das Geschäft sei vollkommen sicher.

Notes

The figurative sense (= excessively flattering, ingratiating) maps most naturally to schleimig in everyday German, though the word is blunter and more overtly contemptuous than oily. For formal or political contexts, aalglatt (literally: smooth as an eel) is the more refined choice: it implies someone is slippery and evasive rather than openly fawning.