1. The quilt club is greatly exciting.

2. The mountain climbing club is badly interesting.

3. The courses and careers club is great fun. (Can we say "...good fun"?)

4. The ping-pong club is exceedingly interesting.

5. The robot manufacture club is terrific.

(Are they all grammatical? I'd like to know more expressions which I can use instead of 'very'. Would you let me know more?)

1 -- The quilting club ...

2 -- The mountain climbing club is very interesting. (You don't want to use "badly" -- it's a negative.)

3 -- I'd change it to just "the careers club" and then use either "great" or "good" before "fun." They mean about the same thing.

4 is fine.

5 -- The robotics club is terrific.

Other than "very," you can also use any of the following, but not always interchangeably:

really
most
exceptionally
fantastically

Here's a thesaurus search for "very" --
http://thesaurus.reference.com/browse/very
If you browse through the adverbs, you'll find LOTS of words, although a few of the longer words will not always work well as a substitute in the sentences you're working with right now.

All of the sentences are grammatically correct. However, some of the phrases might sound a bit unusual due to the combination of adjectives and nouns.

In terms of expressions you can use instead of "very," there are several options to choose from depending on the context and the degree of intensity you want to convey. Here are a few examples:

1. Instead of "greatly exciting," you can use:
- Extremely exciting
- Incredibly exciting
- Intensely exciting

2. Instead of "badly interesting," you can use:
- Extremely interesting
- Fascinatingly interesting
- Profoundly interesting

3. Instead of "great fun" (which is already a common expression), you can use:
- Tremendous fun
- Enormous fun
- Fantastic fun

4. Instead of "exceedingly interesting," you can use:
- Unbelievably interesting
- Remarkably interesting
- Astonishingly interesting

5. Instead of "terrific," you can use:
- Amazing
- Phenomenal
- Spectacular

Remember, each expression has its own level of intensity, so make sure to choose the one that best fits your intended meaning.