Is there a difference between 'Gegenstand', 'Sache', 'Ding', and 'Dinge'? covers 3 of the 5 words I've translated as 'thing'. Based on it and a few sources, these are my guidelines for choosing between these words:
Gegenstand - Tangible object, formal. Used manuals, debates, formal writing and speech, etc.
Sache - Intangible object (e.g. idea, memory, argument)
Ding - Tangible object, informal. Most common word for 'tangible object' in everyday conversation. Used like English 'thing'. (According to wiktionary - 'Ding' and the English 'thing' share an origin)
Objekt - Tangible object, more formal than Ding, but the two are interchangeable. In everyday conversation, this is less common than Ding. Choice between these two is exact same as choice in English - thing or object.
Zeug - Tangible object, informal. Interchangeable with Ding and Objekt. In everyday conversation, this is more common than Objekt, though less than Ding. Of the 'thing' words, Zeug is preferred for compounds (e.g. Flugzeug, Schlagzeug, Bettzeug).
Is my understanding correct? Also, are there any other common words to refer to 'things'?