Why "meth-", "eth-", "prop-", when there is "uni-","di-","tri-"?

Short answer: they were invented to preserve names of organic substances that already were in use. From Wikipedia's article on number prefixes:

The IUPAC nomenclature of organic chemistry uses the numerical prefixes derived from Greek, except for the prefix for 9 (as mentioned) and the prefixes from 1 to 4 (meth-, eth-, prop-, and but-), which are not derived from words for numbers.

These prefixes were invented by the IUPAC, deriving them from the pre-existing names for several compounds that it was intended to preserve in the new system:

• methane (via methyl which is in turn from the Greek word for wine),
• ethane (from ethyl coined by Justus von Liebig in 1834),
• propane (from propionic which is in turn from pro- and the Greek word for fat), and
• butane (from butyl which is in turn from butyric which is in turn from the Latin word for butter).