When native Chinese refer to China, what's the difference between 大陆, 中国 and 中国大陆?
When used with certain words, "中国" may be perceived more as a cultural/historical concept that has a vague boundary on what you want to refer to (the people, the land, the culture, etc).

Example: 周杰倫的中國風音樂／周杰伦的中国风音乐. Jay Chou's Chinese style music. (Jay is a popular artist from Taiwan.) 

In this particular example, 中國 is similar to 中華 (The cultural concept). I think this is because 中国风 implies the usage of traditional style melodies, musical instruments, and lyrics, which is rooted in the cultural artifacts that have been existing for many centuries. The boundaries of "中国" in “中国风” feels vague, just like the bound of "China Proper" has kept changing over the many past centuries.

Another similar example: “中国话／中國話／中文”， the Chinese Language.

This may also happen in the phrase “中国历史”. The "中国" in this particular example would refer to the China encompassing both Mainland and Taiwan before Taiwan was ceded to Japan during the signing of《馬關條約》in year 1895, and/or the China during the Tang dynasty that did not include today's Tibet.
The word "China" may not even just refer to a particular ethnic group, e.g. the Han ethnic group (that accounts for 95%+ of China's population as of today), and the Han has been practically ruled over several times during history. Examples are the fall of the Song dynasty in the 12th century and the fall of the Ming dynasty in the 17th century when the Manchus ruled. (However, the rulers began to use Chinese characters, which is an evidence that some say would justify that they were "assimilated into China", rather than "they annihilated China".) That is another example the word "China" may refer to a concept that has a vague ethnic boundary.

For "大陆", "中国大陆" and when "中国" is used independently today, there shall be an implied geographic bound in today's world, and the bound is usually much more clearly defined, although it may slightly differ on the person's political viewpoint. "中国大陆" and "大陆" are used (only) to refer to People's Republic of China founded in 1949.

A little digression below:

The word "中国" is said to have gained its new meaning --- a modern "country/sovereignty" in 1912 when Republic of China was established, as an abbreviation of 中華民國 (1). Prior to that, "中国" may more often mean "the central area/district/city" or the capital city. Example: 


  “湘娥啼竹素女愁，李憑*中國*彈箜篌" (《李憑箜篌引》， by 李賀, Tang Dynasty) (2)


1) https://zh.wikipedia.org/wiki/%E4%B8%AD%E5%9C%8B#.E8.AF.8D.E6.BA.90

2) https://zh.wikipedia.org/wiki/李凭箜篌引