Stimulants produce euphoria by stimulating the hedonic hotspots in the nucleus accumbens and ventral pallidum (this is a direct and indirect effect of their pharmacodynamics in dopaminergic neurons). Their effects on wakefulness/arousal occurs through the stimulation of the ascending reticular activating system (ARAS) (this is a direct effect of their pharmacodynamics in noradrenergic neurons). GABA is normally released from the ventrolateral preoptic area into the ARAS, which it inhibits. It also acts on other regions of the brain to promote sleep or that are involved in sleep-wake transition (e.g., on the parabrachial nucleus when released from the parafacial zone and on the lateral hypothalamus).
The direct effect of GABA in the striatum is unrelated to sleep/wakefulness because that region of the brain doesn't regulate arousal; however, GABA which is released into the striatum or onto the dopaminergic afferents to the striatum might have an indirect inhibitory effect on arousal via neural networks that connect the striatum to the ARAS.
See links on these sleep-related brain structures:
https://en.wikipedia.org/wiki/Reticular_activating_system
https://en.wikipedia.org/wiki/Lateral_hypothalamus
https://en.wikipedia.org/wiki/Ventrolateral_preoptic_nucleus
https://en.wikipedia.org/wiki/Parafacial_zone
https://en.wikipedia.org/wiki/Parabrachial_area
These are links to articles about the primary GABAergic nucleus that inhibits striatal DA projections in the VTA (and, IIRC, the substantia nigra as well) as well as the VTA dopaminergic projections to the striatum:
https://en.wikipedia.org/wiki/Rostromedial_tegmental_nucleus
https://en.wikipedia.org/wiki/Ventral_tegmental_area