The phrase "a few strides on" is correct and usable in written English.
It can be used to indicate a short distance ahead or to suggest moving forward a little bit in a physical or metaphorical sense.
Example: "After a few strides on the path, we reached a beautiful clearing in the woods."
Alternatives: "a short distance ahead" or "a few steps forward".
"I had to come wide, then I was distracted for a few strides on the home turn when Pat Eddery kept looking down at his horse [Oakley Rambo, who finished last] as if he was going to pull him up.
YOUNGSTOWN, Ohio -- President Obama came Tuesday to this area long synonymous with economic distress to take a few strides on a victory lap for the policies he credits with helping create jobs and to knock Republicans for standing in the way.
Nyquist broke alertly and went to the lead, a position he held except for a few strides on the backstretch when longshot Sawyers Mickey poked his nose in front.
Breaking sharply under Mark Guidry, Balto Star took the lead a few strides out of the gate.
Clearly distraught and sobbing, she tried to keep running but stopped again after a few strides, her hands on her knees.
Mr. Brûlé also masterminded the 26 fliers on display on the wall a few strides past the packing station.
On the next fairway, Johnson was a few strides ahead of the group when he fell back to join Woods and Stricker, who were walking together.
As Cabral leaped to clear the barrier, Kebenei — just a few strides ahead — fell into water.
Again, Hamelin found the smallest of holes, this time just a few strides from the wire.
After passing Cemetery Hill, the last major climb on the Van Cortlandt Park course, Cabral made a strong downhill run and found himself a few strides ahead of Harvard's Dan Chenoweth, the defending champion — "somewhat by accident," he said.
But he strained the hamstring a few strides before reaching first base.
