Both men will go straight into the Glovers' squad for their home date with high-flying MK Dons on Saturday.
Promising striker Obika was the top scorer for Spurs' academy side last season and has been among the goals for the club's reserves this term.
The 18-year-old was also handed a senior debut as a late substitute in a Uefa Cup clash with NEC Nijmegen in November.
His first full start also came in Europe, against Shakhtar Donetsk, and he impressed over the course of his first 90-minute run out.
Townsend, meanwhile, is a left-sided midfielder who was a regular in Spurs' U18 squad last season and travelled with the first team for a pre-season training camp in Spain.
He has won five caps with England's U16 side and was in Tottenham's senior squad for the Uefa Cup clash against Shakhtar in which Obika made his first start.