These logic puzzles are not Nikoli-like. Generally they use clues written out in words.
Building Blocks puzzle: see lettered dice
Castawords puzzle: see lettered dice
Cheryl's Birthday problem
Dicey Words: see lettered dice
Einstein's puzzle: see logic puzzle based on elimination
lettered dice
liar logic puzzles (and self-referential statements, etc.)
logical deduction
logic puzzle based on elimination
ordering logic puzzles
time-sequence puzzles