I am writing a review paper and I came across a literature in which measurement of force is given in pounds and likewise for other quantities. In all the other papers, only the SI system of units is followed. Should I use the units used by the author or should I convert the measurement values to SI units?
To avoid confusion and to ensure the comparability of the results, you should use uniform and consistent units throughout the paper. You can write a note explaining that in the original paper the authors used pounds, furlong per fortnight etc.
And of course, yes, use the SI units. Nowadays all non-SI units are defined in terms of SI units. However, don't trust random sources for the conversion factors: an up-to-date and recommended source for conversion factors is the NIST Guide to the SI, Appendix B: Conversion Factors.
I echo Massimo Ortolano's answer that the most important thing is to be consistent: if you normally use SI units in your article, then you should definitely convert the units from articles that use other systems to the same system as the rest of your article.
However, although this wasn't your actual question, you should not assume that you must always use SI units by default. Although that is indeed the almost universal standard for scientific journals, it is not necessarily the case for non-scientific disciplines (and you didn't specify which discipline you are talking about). In particular, some American journals (probably even some scientific ones) seem to permit non-SI units (for example, the published article you found with non-SI units, though that might possibly be an older article). So, the question of which units to use actually depends on the standards of the specific journal in which you are publishing. You should consult the guide for authors or ask the editor if you have any doubt on this point.