Watch the spelling of 'neither'.
Technically the pattern is "neither...nor...", but you'll often hear "or" instead of "nor" in casual conversation. I'm not sure if that's technically wrong, but it definitely is more casual and (in my opinion) common. Otherwise there's nothing wrong with that phrase.
There are problems with the rest of the sentence though. The quickest way to make the sentence better is to change "to" to "such". "Are becoming" should also be "become" since you're talking about what often happens. You also need to add another comma after 'understand' to make it clear that 'English' is also the subject of 'read':
"However, often all our efforts become such that we can read, but neither speak nor understand, English".
This is now both correct and understandable, but it's still a bit awkward. It'd sound a lot better if you moved 'often' to in-between 'efforts' and 'become'.:
"However, all our efforts often become such that we can read, but neither speak nor understand, English".
If you want to make it slightly less formal, replace "neither...nor..." with "not...or...":
"However, all our efforts often become such that we can read, but not speak or understand, English".