Advancements in microfluidic manipulation devices are vital for the development of future lab-on-a-chip technologies with applications in the biological, chemical, and materials sciences. Surface acoustic wave (SAW)-based acoustofluidic separation devices, using low power densities, offer non-contact and label-free sorting capabilities using differences in mechanical properties (density, compressibility, etc.) or sizes of the micro-objects. A particle suspended in a fluid within a microfluidic channel experiences a direct acoustic radiation force (ARF) when travelling surface acoustic waves (TSAW) couple with the fluid at the Rayleigh angle. Most SAW-based microfluidic devices rely on the horizontal component of the ARF to migrate pre-focused particles laterally across a microchannel width. Although the magnitude of the vertical component of the ARF is more than twice the magnitude of the horizontal component, it has been long ignored due to polydimethylsiloxane (PDMS) microchannel fabrication limitations and difficulties in particle focusing along the vertical direction. In the present work, we have devised a single layered PDMS microfluidic chip for hydrodynamically focusing particles in the vertical plane while explicitly taking advantage of the horizontal ARF component to slow down the selected particles and the stronger vertical ARF component to push the particles in the upward direction to realize continuous particle separation. An acoustofluidic device with a straight PDMS microchannel placed directly on top of a straight interdigitated transducer (IDT) was used to produce high frequency (140 MHz) TSAWs. Contrary to the conventionally used two sheath flows for particle focusing, a single sheath flow was used to pinch the particles close to the bottom of the microchannel. The TSAWs originating from the IDT pushed the focused larger 4.8 $\mu m$ diameter particles in the upward direction to isolate them from smaller 2.0 $\mu m$ or 3.2 $\mu m$ diameter particles. The proposed particle separation device offers high-throughput operation with purity > 97% and recovery rate > 99%. It is simple in its fabrication and versatile due to the single layered microchannel design, combined with vertical hydrodynamic focusing and the use of both the horizontal and vertical components of the ARF. Using the concept of upward migration of particles, another acoustofluidic device was presented for the concentration and separation of four different sized micro-objects inside a single-layered straight polydimethylsiloxane (PDMS) microchannel without using external pumps. Two parallel placed interdigitated transducers (IDTs) were used to produce high frequency (73 MHz & 140 MHz) traveling surface acoustic waves (tSAWs) that trap and concentrate the 12 $\mu m$ and 4.8 $\mu m$ diameter particles at two different locations inside the PDMS microchannel without the assistance of microfabricated PDMS membrane, while allowing the 2.1 $\mu m$ particles to filter through the chromatography of different size microspheres.