Ah, yes the misconceptions I had seem to have been my downfall here. So I can conclude several things (hopefully) correctly:
As electronegativity increases for an atom, so too does stability. This, in turn, creates a weaker base. Thus [OH]- is the weakest base in the original list, followed by [NH2]-. All the carbon containing lewis bases are then stronger.
To compare the basicity of carboanions, you need to consider e-r (the electron radius) and the s character of the orbital. As e-r decreases, stability increases and thus a comparatively weaker base. e-r will decrease with increasing s character, and therefore sp will have the smallest e-r and be a weaker base than a comparative atom that is sp2 and subsequently sp3 hybridized.
Combining these conclusions, my series from weakest to strongest base would be:
[OH]-
[NH2]-
[R-C#C]-
[H2C=CH]-
[CH3-CH2]-
Hopefully my misconceptions are remedied. Thank you for the help.