It's still possible to purchase Wii Points and DSi Points at this current time. Most point cards are off the market though it seems, with the only way to buy them is to visit the shop channels directly and use a credit/debit card.
Side note: I cannot find any information online on Nintendo's website to suggest that the Wii/DSi point system is going offline anytime soon. I have bought points recently. (Picture of points purchase on the new Store and previous store, as by Mint records.)
No, you will not be able to continue to redeem Wii Points once the Wii Shop Channel is discontinued, per the official closure announcement from Nintendo.
The Wii Shop Channel will be closing down on January 30, 2019. Wii Points can continue to be added until March 26, 2018, and content can be purchased with existing points through January 30, 2019.
Nintendo has provided a Q&A with additional details.