Ultralong period radio transients (ULPTs), with periods of thousands of seconds, challenge conventional pulsar models. We propose that these isolated sources are strange dwarf (SD) pulsars—compact objects with a strange quark matter core surrounded by a normal matter crust. We develop a theoretical framework for SD pulsars and apply it to four known isolated ULPTs: GLEAM-X J162759.5–523504.3, GPM J1839–10, ASKAP J1832–0911 (DART J1832–0911), and ASKAP J193505.1+214841.0 (ASKAP J1935+2148). Our analysis shows that SD pulsars naturally explain both the ultralong periods and coherent radio emission of these sources, which occupy a distinctive region in the magnetic field–period diagram. We find that these objects have surface magnetic fields ranging from 10⁶ to 10¹⁰ G, with a consistent lower bound near 10⁶ G that suggests a fundamental threshold for pair production in these magnetospheres. Their radio emission efficiencies (η_rad,rot ≈ 10⁻⁴–10⁻²) align with those of normal pulsars despite their extreme periods. ASKAP J1935+2148 represents a boundary case, positioned below the theoretical death line but still radio active, offering crucial insights into emission mechanisms at extreme periods. The observed X-ray properties of ASKAP J1832–0911, including its two-component spectrum and synchronous X-ray/radio variability, strongly support the SD pulsar model. This framework provides a unified explanation for ULPTs and has significant implications for understanding exotic dense matter in compact objects.