Adjust oven rack to middle position and preheat oven to 350°F (175°C). Spray a 9-by-13-inch baking pan with baking spray; set aside.

In a large bowl with a hand-held electric mixer, or in the bowl of a stand mixer fitted with the whisk attachment, beat butter, 2 cups (14 ounces) sugar, and lemon zest on medium speed until fluffy, 3 to 4 minutes, stopping to scrape down sides of bowl as needed. Add oil and almond extract (if using) and beat on medium speed until combined, about 15 seconds. Add eggs, one at a time, beating just until combined after each addition, about 1 minute.

In a medium bowl, whisk together flour, salt, and baking soda. In a separate small bowl, whisk together sour cream and milk. With mixer on low speed, add about ⅓ of flour mixture to butter, then drizzle in ½ of milk and sour cream mixture. Beat at low speed until just blended after each addition. Repeat adding in increments, beginning and ending with flour mixture, about 3 to 4 minutes total. Spread batter evenly into prepared pan. Firmly tap pan on counter several times to release any large air bubbles trapped in batter.

Bake until cake springs back slightly when touched and a wooden toothpick or cake tester inserted in center comes out clean, 30 to 35 minutes. Let cool in pan on a wire rack for 20 minutes.

Using a handle of a wooden spoon (about (⅜-inch-wide), poke ¾-inch deep holes in cake in about ¾-inch intervals; wipe handle clean as needed.

In a medium microwave safe bowl, microwave preserves and lemon juice together on high power in 15- to 30-second intervals, stirring between each interval, until loosened to a syrup-like consistency, about 1 to 1 ½ minutes total. Spoon strawberry mixture into holes of cake, then spread remainder evenly over top of cake all the way to edges. Let sit, uncovered, on a wire rack at room temperature until completely cooled, about 2 to 3 hours.

When ready to serve, in a large bowl with a hand-held electric mixer, or the bowl of a stand mixer fitted with the whisk attachment, beat cream cheese and remaining 3 tablespoons sugar on medium speed until smooth and creamy, 1 to 2 minutes. With mixer on medium speed gradually add cream and beat until just starting to thicken, 3 to 4 minutes. Increase speed to medium-high and beat until medium-stiff peaks form, 1 to 2 minutes.

Spread whipped cream over cooled cake. Top evenly with sliced berries. Slice and serve.