The CPS linking variables are currently available for all basic monthly samples. You can find the household linking key CPSID here and the person linking key CPSIDP here. These variables are adequate for linking across basic monthly samples. See this answer for background on the inherent complexity of creating these linking keys and its implications for researchers.
Longitudinal weights are not currently available in the IPUMS-CPS dataset. In the meantime, the NBER basic monthly files do contain longitudinal weights for samples from 1989 to present. Because the NBER and IPUMS-CPS files share a common sort order, it is possible to sequentially merge the raw CPS data files from NBER onto an IPUMS-CPS extract (as long as you have not used the select cases option).
There are no Strata/Cluster variables in the CPS public-use files, because they are censored from the data by the Census Bureau. However, the WTFINL variable does account for both Strata and PSU. Therefore, if you are using svyset in STATA, then the WTFINL variable is sufficient. While IPUMS-CPS does not endorse any specific “best practice” method for generating variance estimates, we recommend that users explore current literature on estimating variance in the Current Population Survey. For example, this article describes a procedure for generating synthetic design variables to use in place of the censored variables.
Hope this helps.