Why is my sound coming out weird both from speaker and headphone jack?

It seems from your description that you hear this static noise even when the volume is turned completely off which to me could imply that you are getting some kind of electrical discharge, like for example, jumping across from a component to ground shielding or a piece of metal. If have the unit opened up in a dark room, that effect should be readily apparent and the source identified.

If only hearing it when there is some level of sound volume applied that would probably point to electrical noise/interference being injected into the audio circuitry. In either case though, as a first step in isolating the problem, after powering up the unit and once the noise is apparent, use a non-conductive tool, such as a plastic spudger, to move wires or components and prod cold/cracked solder joints to see if the sound is eliminated or gets worse. If the offending component is found and the situation rectified (ie securing loose wires or connectors etc), then all well and good; if not you will have to used additional troubleshooting methods (for example, signal tracer, oscilloscope, multimeter) to track down the problem.