There ____no eggs or milk in fridge.

If you decide to keep a sentence with a "there is" or "there are" at the beginning,the trick to figuring out what verb to use is to find the real subject of the sentence.
要判断是there is 或是 there are,你首先要看句子的主语是什麼.
Use "there is" for one item.(singular nouns) there is 後接单数可数名词
Use "there is" for non-count items.(non-count nouns) there is 後接不可数名词
Use "there are" for many items.(plural nouns) there are 後接复数可数名词
在你的句子中,there 只是一个expletive word.真正的主词是eggs or milk
eggs 是复数可数名词,但milk是不可数名词,两个在一起怎麼办呢?
依就近原则,there 後面紧跟的是eggs,所以要用are.
So,the sentence should be:
There are no eggs or milk in the fridge.

填 are
no是修饰eggs的。。eggs是主语。。

复数，eggs作主语，就近原则指的是两个名词的情况下
例如：There is one apple and two oranges on the table。

是no 的话 我们老师好像讲的是单复都可以啊。。。

no eggs 表示没有，用单数