To enhance the usually low-charge carrier mobilities of highly twisted donor-acceptor-type compounds that exhibit thermally activated delayed fluorescence, we designed a rodlike acceptor benzodioxinoquinoxaline. This acceptor and two donor-acceptor-donor derivatives were synthesized via microwave Buchwald-Hartwig cross-coupling reactions with yields of up to 91%. The compounds exhibit three different types of photoluminescence, which is well-explained by quantum chemical calculations. Benzodioxinoquinoxaline shows blue fluorescence, with a very short lifetime of 0.64 ns. Its derivatives exhibit either green solid-state-enhanced thermally activated delayed fluorescence (SSE-TADF) or room-temperature phosphorescence (RTP) with lifetimes approaching 7 ms. When molecularly dispersed in a polymeric host, the compounds show a photoluminescence quantum yield close to 60%. The derivatives containing acridine or phenoxazine moieties exhibit bipolar charge transport. At an electric field of 5.8 x 105 V/cm, hole and electron mobilities of the phenoxazine-containing compound reach 3.2 x 10-4 and 1.5 x 10-4 cm2 V-1 s-1, respectively. Among the studied SSE-TADF-based organic light-emitting diodes, the device containing this compound shows the highest external quantum efficiency of 12.3% due to the good charge-transporting and SSE-TADF parameters of the emitter.