What is the argument AGAINST the position that only Paul's writings are applicable to the church today? In mid-Acts dispensationalism (a form of hyperdispensationalism), it is taught that only Paul's writings (from Romans to Philemon) are applicable to the church today and that the other parts of the Bible are informational only.

What is the logical and biblical argument against this position?  I'm interested in an argument that emphasizes Paul's writings themselves.
This was actually the Marcionite position - namely that the Gospel of &quot;grace&quot; as revealed by Paul, superceded everything else.
Marcion's Canon consisted of 10 books - 9 of which were Pauline Epistles and the remaining of which was the Euangelion, a &quot;Gospel&quot; of sorts that rejected the bodily incarnation of Christ and understood the Hebrew Bible to be the result of the demiurge - an evil counterpart to the God who was strictly one of grace.  Indeed, Marcion is often considered one of the first heretics - precisely for believing that only Paul's words were inspired.  (On the bright side, it was his canon that eventually led the church to form a consensus on what the full canon was.)
That early Gnostic tendencies are being rediscovered by moderns who have innovative views of Scripture is not overly remarkable.
The answer, of course, is that Paul himself rejected the later Marcionite position. His warnings against false teachers who taught things other than what Jesus and the Dsiciples did.  He writes in 2 Thessalonians:

But we ought always to thank God for you, brothers and sisters loved by the Lord, because God chose you as first fruits to be saved through the sanctifying work of the Spirit and through belief in the truth. 14 He called you to this through our gospel, that you might share in the glory of our Lord Jesus Christ.
15 So then, brothers and sisters, stand firm and hold fast to the teachings[c] we passed on to you, whether by word of mouth or by letter.

Paul's message shows God's grace, but reminds us as well that God's justice is also a part of his nature.  Indeed, the role of the law is not to be discounted. He writes in Galatians 3:24

So then, the law was our guardian until Christ came, in order that we might be justified by faith.

That isn't a rejection of the law at all.  Grace may be greater than Law, but law is still there!