Harmonic strength is a concept that generally applies to a musical interval. The harmonic strength of an interval measures the degree to which it establishes a tonal center. Intervals corresponding to smaller number ratios in the harmonic series tend to be stronger, whereas intervals involving higher harmonics (larger numbers) tend to be weaker. Stronger intervals tend to overpower weaker ones, and define the tonal center and harmonic context for a chord.
Harmonic strength is not necessarily the same as the influence of an interval on the overall character of a chord or melody. Strongly dissonant intervals, like semitones, are harmonically weak, but their strong dissonance often dominates other more consonant intervals in terms of defining the overall sound or character of a chord.
The assignment of relative strengths of intervals is subjective, especially when dealing with intervals (such as the whole tone in 31-ET) which are poor matches to just intonation. In general, the effective strength of an interval depends on harmonic context and the experience of a person's ear and their perception of music, which is culturally influenced.
Here is a coarse / general ordering which is useful as a starting point. The following list orders the intervals from strongest to weakest.
For simplicity, this list does not contain inversions except those smaller than the perfect fifth. In general, the strength of an interval is similar to the strength of its inversion.