For poems, songs or poems (created with concentrated poetic intent) the terms have these meanings: "Lyrics" = the entire composition. It is most often used in musical contexts. However, many poets think of their creations as songs, so even in the absence of music you can use "lyrics" for poems or excerpts from books or plays that feel musical to you. "Line" = one literal line. In modern terminology, a "line" contains no carriage returns. However, any short excerpt (maybe 2 or 3 lines) can also be thought of as a "line" so long as it contains one coherent thought. "Word" has the dictionary meaning. The previous sentence contains five words. In a discussion of poetry you don't really need "word" other than to talk about details. For example, you might say "these two words rhyme". When you search for a poem, use the word "poem". For example, rather than say "I am looking for the words of Longfellow's poem about daffodils", just say "I am looking for Longfellow's poem about daffodils".

In US English LYRICS or WORDS refer to the words of a song. LINES refers to the words of a play, movie, TV show, etc.