"Eggs" needs an article or a determiner. As the definite article, "the eggs" points to specific eggs that were bought - likely ones that have just been bought. Your example without it is ungrammatical, but you get the idea if I said "I have bought eggs which were out of date" - it could point to eggs I just bought, or an occasion where I bought eggs years ago. You need to specify which eggs. If all of them of off, use "the eggs"; it not all of them are off, use "some eggs".
The same reasoning goes for "money", although there are some idiomatic ways that "money" is used that "eggs" aren't - for example, "I have eggs" means you have some eggs; whereas "I have money" can be taken at face value, or imply that you have a considerable amount of it. Still, if you are referring to specific money, you need a determiner. I would say "some of his money...". You could emphasise the ratio of his business money by saying "most of", or minimise it by saying "part of..."