They can be as long as the don't intersect or touch at any point.
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Skew lines There is a vertical (or horizontal) and a diagonal!
An oblique line can be diagonal, sloping or slanted. It is not vertical, horizontal, parallel or perpendicular.
two diagonal lines that aren't touching
parallel
In the Union Jack, the flag of the United Kingdom, there are no parallel lines. The flag consists of diagonal and perpendicular lines intersecting to form a complex pattern of crosses representing the individual countries of the UK. The red diagonal cross of St. Patrick is superimposed over the diagonal white cross of St. Andrew, which is then superimposed over the vertical and horizontal red cross of St. George.