A CT can show the location of a large stroke and is also useful a quick and cheap test for determining the presence of an hemorrhagic stroke, but it takes longer for an ischemic stroke to be visible on a CT vs. MRI. MRI is also more sensitive a detecting smaller strokes, and other pathology, to answer a question of does my patient need a LP, biopsy, etc. In most cases, radiology has MRI protocols for various differential diagnoses. For ischemic stroke, it's usually T1, T2, FLAIR, DWI and ADC maps. ADC maps are calculated from the DWI to differentiate restricted diffusion from T2 "shine through" on DWI.
Of course, a MRA of the intracranial and extracranial circulation is ordered. A MRA can be done with or without contrast. Other ways of examining the circulation include CT angiography, digital subtraction angiography (requires catheterization), and ultrasound Doppler.
If there is hemorrhage based on CT scan, then add a gradient echo sequence, which may be called susceptibility weighted on certain scanners, to look for microhemorrhages.
For acute stroke, some centers do CT perfusion; others will do MRI perfusion, which is with contrast, to look for a perfusion-diffusion mismatch to stratify patients for endovascular treatment.
This is a brief overview. There is more to learn about MRI from visiting the Radiopaedia site.
Have you though about doing a rotation in radiology or neuroradiology? A neuroradiology rotation would be helpful if you're thinking about going into neurology. There are opportunities for neuroradiology rotations during neurology residency as well.