There are a number of inaccuracies in the reporting.
First, what Trump signed was a series of presidential memorandums, not executive orders. The practical difference between the two doesn't really matter in this case, though.
Second, what you describe is actually two different memorandums.
The first, deferring the payment of payroll taxes, is probably within his powers (Trump cites 26 USC 7508A, which gives the Secretary of the Treasury the ability to defer tax payments in the event of a disaster). But it's also highly counterproductive: the taxes still need to be paid. On December 31, when the deferment expires, the tax bill comes due. For the typical person, this bill equals about three weeks' pay -- and it's now being paid in a single lump rather than being spread out over four months.
The second, supplemental unemployment insurance payments, is questionable at best. He's directing that FEMA disaster-relief funds be used to provide unemployment payments, and ordering the states to match that money 1 for 3 out of unspent CARES funds. This is almost certainly not within his powers. He's citing 42 USC 5174(e)(2) as the source of authority, but "other necessary expenses or serious needs" is intended to cover specific needs, not no-questions-asked payments. The 1:3 match ratio is covered by 42 USC 5174(g)(2) requiring states to provide 25% of the money distributed under 42 USC 5174(e), but it does not say where the states need to get that money from.
Like the first, this program, even if legal, is likely to be counterproductive. Trump is drawing down FEMA's funds just as a very active Atlantic hurricane season is picking up steam.
The Secretaries of Labor, Treasury, Homeland Security, and the administrator of FEMA all have standing to challenge this, as they're the ones the memorandums are addressed to -- but it's unlikely they'll do so. Congress as a whole has standing, since this may be infringing on their powers under the Constitution. The individual houses of Congress may have standing, as may individual members, but this is unsettled.