Quantification of EST/cDNA based retained intron transcripts
You can do full-length whole-transcriptome sequencing using either the direct RNA kit or a cDNA kit (with or without PCR) on a MinION. This will allow you to quantify isoforms directly, rather than estimating by looking at read pairs.

However, it'd be a bit expensive to do it that way if you're looking at a single transcript (and aren't barcoding to multiplex samples on the same run).

If you've already done Illumina whole-transcriptome sequencing (e.g. strand-specific paired-end sequencing), tools like Kallisto, RSEM, or Salmon can be used to estimate isoform expression based on the mapped reads. These tools use the information about transcript placement and/or similarity to alter the observed read counts in an attempt to better represent reality.

Unfortunately, if you want these tools to quantify intronic sequence (i.e. the $2^4$ possibilities you have suggested), then those sequences need to be included in the sequences provided. They won't estimate frequencies for non-existent sequence.

As an alternative to including every possible gene model, something like a SuperTranscript model might work. I'm not familiar with Alicia Oshlack's method, but it at least gives the appearance that it might reduce the complexity of searching for multiple unannotated isoforms within a gene.